Normal Line to a Tangent

Key Questions

• How do you find the equation of a normal line if you know the equation of the tangent line?

  If a tangent line has the equation

  #y-y_1=m(x-x_1)#,

  then the normal line at the point of contact is

  #y-y_1=-1/m(x-x_1)#.

  ---

  I hope that this was helpful.

  Wataru · · Oct 19 2014
• If my tangent line at point (4,8) has the equation #y=5x/6 - 9#, what is the equation of the normal line at the same point?

  The normal line is the line that is perpendicular to the the tangent line.

  If the slope of a line is #m# then the slope of the perpendicular line is #-1/m#, this is also known as the negative reciprocal.

  The given equation is #y=5/6x-9# the slope is #5/6# so the slope of the normal is #-6/5#.

  The point #(x,y)->(4,8)#

  #y=mx+b -># Substitute in the values of #m#, #x# and #y#

  #8=-6/5(4)+b#

  #8=-24/5+b#

  #24/5+8=b#

  #24/5+40/5=b#

  #64/5=b#

  The equation of the normal line is #-> y=-6/5x+64/5#

  AJ Speller · · Oct 11 2014
• What is a Normal Line to a Tangent?

  A normal line is the line perpendicular to a tangent line at the point of contact.

  Wataru · · Sep 11 2014

• What is a Normal Line to a Tangent?
• What is a Normal Line to a curve?
• How you would find the equation of a line normal to a curve?
• How do you find the equation of a normal line to a curve at a given point?
• How do you give the equation of the normal line to the graph of #y=2xsqrt(x^2+8)+2# at point (0,2)?
• What are some applications in which you need to find the normal to the tangent line?
• How do you find the equation of the tangent line and normal line to the curve #y = (5+6x)^2# at the point (-4,361)?
• What is the normal line to the tangent line at a point on a curve?
• What is the equation of the normal line of #f(x)=x^3 + 3x^2 + 7x - 1 # at #x=-1 #?
• What is the equation of the normal line of #f(x)=x^3/(3x^2 + 7x - 1 # at #x=-1 #?
• What is the equation of the normal line of #f(x)=x^3*(3x - 1) # at #x=-2 #?
• What is the equation of the normal line of #f(x)=-4x-10 # at #x=-2 #?
• What is the equation of the normal line of #f(x)= -2x^3-10x # at #x=2 #?
• What is the equation of the normal line of #f(x)= -2x^2-10/x # at #x=2 #?
• What is the equation of the normal line of #f(x)= -3x^2 # at #x=0 #?
• What is the equation of the normal line of #f(x)=(2+x)e^-x # at #x=0 #?
• What is the equation of the normal line of #f(x)=x^2 # at #x=5 #?
• What is the equation of the normal line of #f(x)=sqrt(x/(x+1) # at #x=4 #?
• What is the equation of the normal line of #f(x)=x/(x-1) # at #x=4 #?
• What is the equation of the normal line of #f(x)=(x-1)(x+4)(x-2) # at #x=3 #?
• What is the equation of the normal line of #f(x)=(x-1)(x-3)(x+2) # at #x=3 #?
• What is the equation of the normal line of #f(x)=sqrt(3x^2+2x)# at #x=2 #?
• What is the equation of the normal line of #f(x)=1/sqrt(x^2-2x+1)# at #x=2 #?
• What is the equation of the normal line of #f(x)=x/sqrt(x+1/x)# at #x=2 #?
• What is the equation of the normal line of #f(x)=(x-1)^2/(x-5)# at #x=4 #?
• What is the equation of the normal line of #f(x)=e^x/x# at #x=1 #?
• What is the equation of the normal line of #f(x)=xe^x# at #x=3 #?
• What is the equation of the normal line of #f(x)=xlnx# at #x=3 #?
• What is the equation of the normal line of #f(x)=x/lnx# at #x=4 #?
• What is the equation of the normal line of #f(x)=ln2x-x# at #x=4 #?
• What is the equation of the normal line of #f(x)=xln(3^(1/x))# at #x=9#?
• What is the equation of the normal line of #f(x)=xln(3^(1/x))# at #x=0#?
• What is the equation of the normal line of #f(x)=(1-x)e^(3x)-e^x# at #x=1#?
• What is the equation of the normal line of #f(x)= (1+2x)^2# at #x=1#?
• What is the equation of the normal line of #f(x)= (1+2x)*e^(x^2)# at #x=-1/2#?
• What is the equation of the normal line of #f(x)= (x^2 + 2x - 1)/(4 - 3x) # at #x=-1#?
• What is the equation of the normal line of #f(x)=sqrt(16x^4-x^3# at #x=4#?
• What is the equation of the normal line of #f(x)=x^3/sqrt(16x^2-x)# at #x=2#?
• What is the equation of the normal line of #f(x)=(5+4x)^2# at #x=7#?
• What is the equation of the normal line of #f(x)=((5-x)(4-x^2))/(x^3-1)# at #x=3#?
• What is the equation of the normal line of #f(x)= 3x - 2x^2# at #x=1#?
• What is the equation of the normal line of #f(x)= x^8 + 6 e^x # at #x=0#?
• What is the equation of the normal line of #f(x)= x^e/e^x # at #x=e#?
• What is the equation of the normal line of #f(x)= x^e*e^x # at #x=3#?
• What is the equation of the normal line of #f(x)= 2(x-2)^4+(x-1)^3+(x-3)^2# at #x=4#?
• What is the equation of the normal line of #f(x)= 1-x-x^(1/3)# at #x=1#?
• What is the equation of the normal line of #f(x)=(x^2-1)^(1/3)# at #x=3#?
• What is the equation of the normal line of #f(x)=2x+3/x# at #x=1#?
• What is the equation of the normal line of #f(x)=x-x^2/2# at #x=2#?
• What is the equation of the normal line of #f(x)=x^2-4x# at #x=1#?
• What is the equation of the normal line of #f(x)=x^2/(4x-1)# at #x=4#?
• What is the equation of the normal line of #f(x)=(x-2)/(x-3)^2# at #x=5#?
• What is the equation of the normal line of #f(x)= x^2 − 5x + 1# at #x = 5#?
• What is the equation of the normal line of #f(x)= x^2/(x^3− 5x + 1)# at #x = 5#?
• What is the equation of the normal line of #f(x)= sqrt(x/(x^3− 1))# at #x = 2#?
• What is the equation of the normal line of #f(x)= sinx# at #x = pi/8#?
• What is the equation of the normal line of #f(x)= cosx# at #x = pi/8#?
• What is the equation of the normal line of #f(x)= tanx# at #x = pi/8#?
• What is the equation of the normal line of #f(x)= cotx# at #x = pi/8#?
• What is the equation of the normal line of #f(x)= secx# at #x = pi/8#?
• What is the equation of the normal line of #f(x)= cscx# at #x = pi/8#?
• What is the equation of the normal line of #f(x)= tanx*sinx# at #x = pi/8#?
• What is the equation of the normal line of #f(x)= (1-x)sinx# at #x = pi/8#?
• What is the equation of the normal line of #f(x)= sinx-cos2x# at #x = pi/8#?
• What is the equation of the normal line of #f(x)= xsinx-cos^2x# at #x = pi/8#?
• What is the equation of the normal line of #f(x)= tan(2x)/cotx# at #x = pi/8#?
• What is the equation of the normal line of #f(x)= x/sqrtsinx# at #x = pi/8#?
• What is the equation of the normal line of #f(x)= 3lnsin2x# at #x = pi/8#?
• What is the equation of the normal line of #f(x)= 3xlnsin(2/x)# at #x = pi/8#?
• What is the equation of the normal line of #f(x)= secxtanx# at #x = pi/8#?
• What is the equation of the normal line of #f(x)= (x^2-x)/(x-3)# at #x = 4#?
• What is the equation of the normal line of #f(x)= x^3-3x^2-2x+6# at #x = 4#?
• What is the equation of the normal line of #f(x)= x^3/(3x^2-2x)+6x# at #x = 2#?
• What is the equation of the normal line of #f(x)= (3x^2-2)/(6x)# at #x = 1#?
• What is the equation of the normal line of #f(x)= sqrt(e^(2x)-x^2)/(x-1)^2# at #x = 3#?
• What is the equation of the normal line of #f(x)= e^(x^2-x+3)# at #x = 2#?
• What is the equation of the normal line of #f(x)= e^(x^2+x-12)# at #x = 3#?
• What is the equation of the normal line of #f(x)= e^(x^2/(x-2))# at #x = 3#?
• What is the equation of the normal line of #f(x)= 1+1/(1+1/x)# at #x = 1#?
• What is the equation of the normal line of #f(x)= x+x/(1+x/(1+1/x))# at #x = 1#?
• What is the equation of the normal line of #f(x)= xln(1/x^2)# at #x = 2#?
• What is the equation of the normal line of #f(x)= -xln(4^(1-x))# at #x = 1#?
• What is the equation of the normal line of #f(x)=x^2-x+1/x# at #x = 2#?
• What is the equation of the normal line of #f(x)=sqrt(x-1)/(x^2-3)# at #x = 2#?
• What is the equation of the normal line of #f(x)=1/x^2-x# at #x = 4#?
• What is the equation of the normal line of #f(x)=1/(2x^2-1)# at #x = 1#?
• What is the equation of the normal line of #f(x)=x/(2-x^2)# at #x = 3#?
• What is the equation of the normal line of #f(x)=sqrt(e^x-x+1)/e^(2x)# at #x = 0#?
• What is the equation of the normal line of #f(x)=(x-3e^x)^(1/2)-x^2# at #x = -3#?
• What is the equation of the normal line of #f(x)=(x+e^(1/x))^(3/2)-x# at #x = 4#?
• What is the equation of the normal line of #f(x)=x^2# at #x=-5#?
• What is the equation of the normal line of #f(x)=e^-x+x^3# at #x=-5#?
• What is the equation of the normal line of #f(x)=x^3e^-x+x^3# at #x=-5#?
• What is the equation of the normal line of #f(x)=xe^-x-x# at #x=2#?
• What is the equation of the normal line of #f(x)=e^(2x)-x^3# at #x=2#?
• What is the equation of the normal line of #f(x)=xlnx-e^-x# at #x=2#?
• What is the equation of the normal line of #f(x)=x^2-x+5# at #x=2#?
• What is the equation of the normal line of #f(x)=-4x-1# at #x=2#?
• What is the equation of the normal line of #f(x)=sqrt(x^3-x+4)# at #x=2#?
• What is the equation of the normal line of #f(x)=(x-2)^(3/2)-x^3# at #x=2#?
• What is the equation of the normal line of #f(x)=sqrt(x^2-x)# at #x=2#?
• What is the equation of the normal line of #f(x)=sqrt(2x^2-x)# at #x=-1#?
• What is the equation of the normal line of #f(x)=(x-3)^3(x+2)# at #x=-1#?
• What is the equation of the normal line of #f(x)=(x-3)^3(x+2)# at #x=0#?
• What is the equation of the normal line of #f(x)=(x-4)e^(x-2)# at #x=0#?
• What is the equation of the normal line of #f(x)=(x^2-4)-e^(x+2)# at #x=2#?
• What is the equation of the normal line of #f(x)=e^(4x)/(4x)# at #x=-1#?
• What is the equation of the normal line of #f(x)=e^(4+x)/(4-x)# at #x=0#?
• What is the equation of the normal line of #f(x)=e^x-x^3# at #x=0#?
• What is the equation of the normal line of #f(x)=1/(1-2e^(3x)# at #x=0#?
• What is the equation of the normal line of #f(x)=1/(1-2e^(x)# at #x=-1#?
• What is the equation of the normal line of #f(x)=x^2/(1+4x)# at #x=-1#?
• What is the equation of the normal line of #f(x)=(x-3)/(x+4)# at #x=-1#?
• What is the equation of the normal line of #f(x)=(x-3)/(x+4)# at #x=3#?
• What is the equation of the normal line of #f(x)=(x+2)/(x-4)# at #x=3#?
• What is the equation of the normal line of #f(x)=(x-9)^2/(x-1)# at #x=-2#?
• What is the equation of the normal line of #f(x)=x-sinx# at #x=pi/6#?
• What is the equation of the normal line of #f(x)=x/sinx# at #x=pi/6#?
• What is the equation of the normal line of #f(x)=sinx# at #x=pi/6#?
• What is the equation of the normal line of #f(x)=tanx# at #x=pi/6#?
• What is the equation of the normal line of #f(x)=1/sinx+cscx# at #x=pi/6#?
• What is the equation of the normal line of #f(x)=cos(2x-pi/2)# at #x=pi/6#?
• What is the equation of the normal line of #f(x)=1-x/lnx# at #x=2#?
• What is the equation of the normal line of #f(x)=1-lnx/x# at #x=1#?
• What is the equation of the normal line of #f(x)=1/x-lnx/x# at #x=1#?
• What is the equation of the normal line of #f(x)=(x+5)/(e^x-1)# at #x=1#?
• What is the equation of the normal line of #f(x)= (x-1)e^(-x^3-x) # at #x=1#?
• What is the equation of the normal line of #f(x)= 1/xe^(-x^3+x^2) # at #x=-1#?
• What is the equation of the normal line of #f(x)= 1/x-e^(-x^3+x^2) # at #x=-1#?
• What is the equation of the normal line of #f(x)=e^(1/x)-x# at #x=-1#?
• What is the equation of the normal line of #f(x)=xe^(1/x)-x^2-3# at #x=0#?
• What is the equation of the normal line of #f(x)=4x-x^2# at #x=0#?
• What is the equation of the normal line of #f(x)=3^x-x# at #x=-3#?
• What is the equation of the normal line of #f(x)=ln(1/x)# at #x=5#?
• What is the equation of the normal line of #f(x)=xln(1/x)-1/x# at #x=5#?
• What is the equation of the normal line of #f(x)=x^3-x^2+6x-1# at #x=5#?
• What is the equation of the normal line of #f(x)=-2x^3-4x^2+6x-1# at #x=2#?
• What is the equation of the normal line of #f(x)=-2x^3+x^2-2x-1# at #x=-2#?
• What is the equation of the normal line of #f(x)=2x^3-8x^2+2x-1# at #x=-1#?
• What is the equation of the normal line of #f(x)=2x^3-x^2-3x+9# at #x=-1#?
• What is the equation of the normal line of #f(x)=x^3-x^2+8x-9# at #x=-1#?
• What is the equation of the normal line of #f(x)=x^3-11x^2-5x-2# at #x=0#?
• What is the equation of the normal line of #f(x)=5x^3+x^2-5x-2# at #x=2#?
• What is the equation of the normal line of #f(x)=5x^3+2x^2+x-2# at #x=2#?
• What is the equation of the normal line of #f(x)=5x^3+3x^2+x-5# at #x=2#?
• What is the equation of the normal line of #f(x)=6x^3-12x^2-x-1# at #x=2#?
• What is the equation of the normal line of #f(x)=-x^4+4x^3-x^2+5x-6# at #x=2#?
• What is the equation of the normal line of #f(x)=5x^4+3x^3+x^2-2x-4# at #x=1#?
• What is the equation of the normal line of #f(x)=-x^4+2x^3+2x^2-x-4# at #x=1#?
• What is the equation of the normal line of #f(x)=-x^4-2x^3-5x^2+3x+3# at #x=1#?
• What is the equation of the normal line of #f(x)=2x^4+4x^3-2x^2-3x+3# at #x=1#?
• What is the equation of the normal line of #f(x)=2x^4+4x^3-2x^2-3x+3# at #x=-1#?
• What is the equation of the normal line of #f(x)=-x^4+2x^3-12x^2-13x+3# at #x=-1#?
• What is the equation of the normal line of #f(x)=-x^4+2x^3-x^2-9x-3# at #x=-1#?
• What is the equation of the normal line of #f(x)=4x^4+8x^3-2x^2+x-3# at #x=-1#?
• What is the equation of the normal line of #f(x)=x^3-x^2+17x# at #x=7#?
• What is the equation of the normal line of #f(x)=x^3-49x^2+7x# at #x=7#?
• What is the equation of the normal line of #f(x)=x^3-4x^2+7x# at #x=-2#?
• What is the equation of the normal line of #f(x)=12x^3-4x^2-5x# at #x=-2#?
• What is the equation of the normal line of #f(x)=-2x^3+18x^2-25x# at #x=-1/3#?
• What is the equation of the normal line of #f(x)=-2x^3-8x^2-2x# at #x=-1#?
• What is the equation of the normal line of #f(x)=x^3+6x^2-3x# at #x=-1#?
• What is the equation of the normal line of #f(x)=2x^3+3x^2-2x# at #x=-1#?
• What is the equation of the normal line of #f(x)=-2x^3+4x^2+2x# at #x=-1#?
• What is the equation of the normal line of #f(x)=x^3-8x^2+9x-3# at #x=-1#?
• What is the equation of the normal line of #f(x)=5x^3-2x^2-3x-1# at #x=-8#?
• What is the equation of the normal line of #f(x)=-7x^3-x^2-x-1# at #x=-8#?
• What is the equation of the line normal to # f(x)=x^2/e^x-x/e^(x^2) # at # x=0#?
• What is the equation of the line normal to # f(x)=(x-1)(x+2) # at # x=0#?
• What is the equation of the line normal to # f(x)=(x-1)(x+2)^2 # at # x=1#?
• What is the equation of the line normal to # f(x)=(x^2-x)(x-2) # at # x=1#?
• What is the equation of the line normal to # f(x)=x(x-2) # at # x=2#?
• What is the equation of the line normal to # f(x)=x^2(x-2) # at # x=2#?
• What is the equation of the line normal to # f(x)=x^2-x-2 # at # x=2#?
• What is the equation of the line normal to # f(x)=4x^2-3x-2 # at # x=3#?
• What is the equation of the line normal to # f(x)=4x^2-3x # at # x=1#?
• What is the equation of the line normal to # f(x)=x/(x-2) # at # x=1#?
• What is the equation of the line normal to # f(x)=1/(x-2) # at # x=1#?
• What is the equation of the line normal to # f(x)=1/(x^2-2) # at # x=1#?
• What is the equation of the line normal to # f(x)=x/(x^2-2) # at # x=1#?
• What is the equation of the line normal to # f(x)=(x-1)/(x^2-2) # at # x=1#?
• What is the equation of the line normal to # f(x)=(x-1)^2/(x^2+2) # at # x=1#?
• What is the equation of the line normal to # f(x)=sqrt(1/(x^2+2) # at # x=1#?
• What is the equation of the line normal to # f(x)=sqrt(1/(x+2) # at # x=-1#?
• What is the equation of the line normal to # f(x)=sqrt(x/(x+2) # at # x=-3#?
• What is the equation of the line normal to # f(x)=x^2-xsinx# at # x=-3#?
• What is the equation of the line normal to # f(x)=x^2sinx# at # x=pi/3#?
• What is the equation of the line normal to # f(x)=sin(2x+pi)# at # x=pi/3#?
• What is the equation of the line normal to # f(x)=sin(x/2+pi)# at # x=pi/3#?
• What is the equation of the line normal to # f(x)=cos(5x+pi/4)# at # x=pi/3#?
• What is the equation of the line normal to # f(x)=xsin(3x+pi/4)# at # x=pi/2#?
• What is the equation of the line normal to # f(x)=xtanx# at # x=pi/2#?
• What is the equation of the line normal to # f(x)=xtanx# at # x=pi/3#?
• What is the equation of the line normal to # f(x)=x/tanx# at # x=pi/3#?
• What is the equation of the line normal to # f(x)=(x-sinx)/tanx# at # x=pi/3#?
• What is the equation of the line normal to # f(x)=(xsinx)/tanx# at # x=pi/3#?
• What is the equation of the line normal to # f(x)=tan^2x-3x# at # x=pi/3#?
• What is the equation of the line normal to # f(x)=cot^2x-x^2# at # x=pi/3#?
• What is the equation of the line normal to # f(x)=x^2cot^2x# at # x=pi/3#?
• What is the equation of the line normal to # f(x)=secx-cot^2x# at # x=pi/3#?
• What is the equation of the line normal to # f(x)=sec4x-cot2x# at # x=pi/3#?
• What is the equation of the line normal to # f(x)=lnx-x^3# at # x=1#?
• What is the equation of the line normal to # f(x)=xln(x^3-x)# at # x=1#?
• What is the equation of the line normal to # f(x)=-xln(2x^3-x)# at # x=1#?
• What is the equation of the line normal to # f(x)=-x/ln(2x^3-x)# at # x=1#?
• What is the equation of the line normal to # f(x)=ln(xe^(3x))# at # x=1#?
• What is the equation of the line normal to # f(x)=ln(x+xe^(3x))# at # x=2#?
• What is the equation of the line normal to # f(x)=lnx-x# at # x=2#?
• What is the equation of the line normal to # f(x)=lnx-1/x# at # x=3#?
• What is the equation of the line normal to # f(x)=lnx^2-1/x^2# at # x=-2#?
• What is the equation of the line normal to # f(x)=sqrt(lnx)# at # x=4#?
• What is the equation of the line normal to # f(x)=e^(sqrtx)# at # x=4#?
• What is the equation of the line normal to # f(x)=e^(sqrtx-x)# at # x=4#?
• What is the equation of the line normal to # f(x)=e^(sqrtx/x)# at # x=4#?
• What is the equation of the line normal to # f(x)=e^(xsqrtx)# at # x=4#?
• What is the equation of the line normal to # f(x)=sqrt(e^(sqrtx)# at # x=4#?
• What is the equation of the line normal to # f(x)=sqrt(x)-e^(sqrtx)# at # x=1#?
• What is the equation of the line normal to # f(x)=xe^(sqrtx)# at # x=1#?
• What is the equation of the line normal to # f(x)=xsqrtx-e^(sqrtx)# at # x=1#?
• What is the equation of the line normal to # f(x)=(x-3)^2+4x# at # x=1#?
• What is the equation of the line normal to # f(x)=(2x-2)^2+4x# at # x=-3#?
• What is the equation of the line normal to # f(x)=2(x-1)^2-2x+4# at # x=-3#?
• What is the equation of the line normal to # f(x)=2/(x-1)^2-2x+4# at # x=-2#?
• What is the equation of the line normal to # f(x)=3(x-1)^2-6x+4# at # x=-2#?
• What is the equation of the line normal to # f(x)=(x-4)(x-2)+2x+4# at # x=-2#?
• What is the equation of the line normal to # f(x)=(x-4)(x-2)+2x^2-3x+4# at # x=0#?
• What is the equation of the line normal to # f(x)=(x+5)(x+2)+2x^2-8x+2# at # x=0#?
• What is the equation of the line normal to # f(x)=-(x+6)(x+3)+4x^2-8x+2# at # x=0#?
• What is the equation of the line normal to # f(x)=-(x-1)(x+3)+4x^2-8x+2# at # x=0#?
• What is the equation of the line normal to # f(x)=-sqrt((x-1)(x+3)# at # x=0#?
• What is the equation of the line normal to # f(x)=-sqrt((x+1)(x+3)# at #x=0#?
• What is the equation of the line normal to # f(x)=-sqrt((x+1)(x+3)# at # x=0#?
• What is the equation of the line normal to # f(x)=-sqrt((x+1)(x-2)# at # x=6#?
• What is the equation of the line normal to # f(x)=-sqrt((x-5)(x-2)# at # x=6#?
• What is the equation of the line normal to # f(x)=-x/sqrt((x-5)(x+2)# at # x=6#?
• What is the equation of the line normal to # f(x)=-x/(x+4)# at # x=6#?
• What is the equation of the line normal to # f(x)=1/(e^x+4)# at # x=6#?
• What is the equation of the line normal to # f(x)=e^(2x)/(e^x+4)# at # x=2#?
• What is the equation of the line that is normal to #f(x)=(x+4)^2-e^x# at # x=-3 #?
• What is the equation of the line that is normal to #f(x)=(x+4)^2e^x# at # x=-3 #?
• What is the equation of the line that is normal to #f(x)=(x+4)^2/e^x# at # x=-1 #?
• What is the equation of the line that is normal to #f(x)=(2x-4)^2/e^x# at # x=2 #?
• What is the equation of the line that is normal to #f(x)=(2x-1)/e^x# at # x=1/2 #?
• What is the equation of the line that is normal to #f(x)=2x^3-3x^2+5# at # x=1 #?
• What is the equation of the line that is normal to #f(x)=4x^3-3x^2+5x-2# at # x=1 #?
• What is the equation of the line that is normal to #f(x)=-2x^3-3x^2+5x-2# at # x=1 #?
• What is the equation of the line that is normal to #f(x)=-2x^3+4x-2 # at # x=-2 #?
• What is the equation of the line that is normal to #f(x)=-2x^2+4x-2 # at # x=3 #?
• What is the equation of the line that is normal to #f(x)=-2x^2-2e^x # at # x=-2 #?
• What is the equation of the line that is normal to #f(x)=-e^x # at # x=-2 #?
• What is the equation of the line that is normal to #f(x)=-3x^2-4x # at # x=-2 #?
• What is the equation of the line that is normal to #f(x)=-3x^2sinx # at # x=pi/3#?
• What is the equation of the line that is normal to #f(x)=-3x^2-sinx # at # x=pi/3#?
• What is the equation of the line that is normal to #f(x)=-sinx +tanx # at # x=-pi/3#?
• What is the equation of the line that is normal to #f(x)=e^xcos^2x -xsinx # at # x=-pi/3#?
• What is the equation of the line that is normal to #f(x)=x^2cosx+sinx # at # x=-pi/3#?
• What is the equation of the line that is normal to #f(x)=cscx+cotx # at # x=-pi/3#?
• What is the equation of the line that is normal to #f(x)=cscx+tanx-cotx # at # x=-pi/3#?
• What is the equation of the line that is normal to #f(x)=sinx-e^xcotx # at # x=pi/3#?
• What is the equation of the line that is normal to #f(x)=sin^2x+e^xcotx # at # x=pi/3#?
• What is the equation of the line that is normal to #f(x)= -xsin^2x# at # x=(4pi)/3 #?
• What is the equation of the line that is normal to #f(x)= cosx-sin^2x# at # x=(4pi)/3 #?
• What is the equation of the line that is normal to #f(x)= cosx-sin2x# at # x=(4pi)/3 #?
• What is the equation of the line that is normal to #f(x)= tanx-sin2x# at # x=(4pi)/3 #?
• What is the equation of the line that is normal to #f(x)= ln(sin^2x) # at # x=(4pi)/3 #?
• What is the equation of the line that is normal to #f(x)= x^3-5x+2 # at # x=3 #?
• What is the equation of the line that is normal to #f(x)= 3(x-2)^2-5x+2 # at # x=3 #?
• What is the equation of the line that is normal to #f(x)= (x+2)^2-5x+2 # at # x=3 #?
• What is the equation of the line that is normal to #f(x)= (x+2)^2-2x^2+2 # at # x=-1 #?
• What is the equation of the line that is normal to #f(x)= (x-3)^2-2x-2 # at # x=-1 #?
• What is the equation of the line that is normal to #f(x)= (x-3)^2+x^2-6x# at # x=0 #?
• What is the equation of the line that is normal to #f(x)= x^3-4x# at # x=0 #?
• What is the equation of the line that is normal to #f(x)= sqry(x-2) # at # x=5 #?
• What is the equation of the line that is normal to #f(x)= sqrt( x^3-3x+2) # at # x=5 #?
• What is the equation of the line that is normal to #f(x)= sqrt( x^2+3x+2) # at # x=1 #?
• What is the equation of the line that is normal to #f(x)= sqrt( 3x+2) # at # x=1 #?
• What is the equation of the line that is normal to #f(x)= xsqrt( 3x+2) # at # x=1 4 #?
• What is the equation of the line that is normal to #f(x)= x-sqrt( 3x+2) # at # x=4 #?
• What is the equation of the line that is normal to #f(x)= x/sqrt( 3x+2) # at # x=4 #?
• What is the equation of the line that is normal to #f(x)= x/sqrt( x^2-2) # at # x=2 #?
• What is the equation of the line that is normal to #f(x)= x/sqrt( 2x+2) # at # x=2 #?
• What is the equation of the line that is normal to #f(x)= (2-x)sqrt( 2x+2) # at # x=2 #?
• What is the equation of the line that is normal to #f(x)= (2-x)/sqrt( 2x+2) # at # x=2 #?
• What is the equation of the line that is normal to #f(x)= (2-x)- sqrt( 2x+2) # at # x=1 #?
• What is the equation of the line that is normal to #f(x)= e^(2x) sqrt( 2x+2) # at # x=1 #?
• What is the equation of the line that is normal to #f(x)= e^(2x-2) sqrt( 2x-2) # at # x=1 #?
• What is the equation of the line that is normal to #f(x)= e^(2x-2) /sqrt( 2x-2) # at # x=3 #?
• What is the equation of the line that is normal to #f(x)= e^(2x-2) # at # x= 1 #?
• What is the equation of the line that is normal to #f(x)= xe^(2x-2) # at # x= 1 #?
• What is the equation of the line that is normal to #f(x)= x/e^(2x-2) # at # x= 1 #?
• What is the equation of the line that is normal to #f(x)= (2x-2)/e^(2x-2) # at # x= 1 #?
• What is the equation of the line that is normal to #f(x)= (2x-2)e^(2x-2) # at # x= 1 #?
• What is the equation of the line that is normal to #f(x)= lnx^2-x# at # x= 1 #?
• What is the equation of the line that is normal to #f(x)= ln(x^2-x)# at # x= 1 #?
• What is the equation of the line that is normal to #f(x)= ln(x^2-x+1) #at # x= 1 #?
• What is the equation of the line that is normal to #f(x)= ln(x^2-x+1)/x #at # x= 1 #?
• What is the equation of the line that is normal to #f(x)= ln(x^2+1)-2x #at # x= 1 #?
• What is the equation of the line that is normal to #f(x)= x^3 ln(x^2+1)-2x #at # x= 1 #?
• What is the equation of the line that is normal to #f(x)= x^3 ln(x^2+1)-x/(x^2+1) #at # x= 1 #?
• What is the equation of the line that is normal to #f(x)= x^3 -ln(x^2+1) # at # x= 2 #?
• What is the equation of the line that is normal to #f(x)= x^3e^sqrtx # at # x= 2 #?
• What is the equation of the line that is normal to #f(x)= xe^sqrtx # at # x= 2 #?
• What is the equation of the line that is normal to #f(x)= x-e^sqrt(x+4)/(x-4) # at # x= 5 #?
• What is the equation of the line that is normal to #f(x)= x(x-4) # at # x= 5 #?
• What is the equation of the line normal to #f(x)=6x^3-8# at #x=7#?
• What is the equation of the line normal to #f(x)=2 tan(pix -2)# at #x=2#?
• What is the equation of the line normal to #f(x)=- tan(2pix -2)# at #x=3#?
• What is the equation of the line normal to #f(x)=x^2+8x - 12# at #x=3#?
• What is the equation of the line normal to #f(x)=x^2+8x - 1# at #x=5#?
• What is the equation of the line normal to #f(x)=2x^2-x - 1# at #x=5#?
• What is the equation of the line normal to #f(x)=-x^2+3x - 1# at #x=-1#?
• What is the equation of the line normal to #f(x)=(x+1)^2# at #x=-1#?
• What is the equation of the line normal to #f(x)=(x+1)^2-4x+5# at #x=-2#?
• What is the equation of the line normal to #f(x)=(x-1)^2-2x+5# at #x=-2#?
• What is the equation of the line normal to #f(x)=(2x^2 + 1) / x# at #x=-2#?
• What is the equation of the line normal to #f(x)=(2x^2 + 1) / x# at #x=-1#?
• What is the equation of the line normal to #f(x)=(3x-1)(2x+4)# at #x=0#?
• What is the equation of the line normal to #f(x)=(3x-1)(x+4)# at #x=-3#?
• What is the equation of the line normal to #f(x)=4/(2x-1) # at #x=0#?
• What is the equation of the line normal to #f(x)=4/(x^3-1) # at #x=0#?
• What is the equation of the line normal to #f(x)=(5+4x)^2 # at #x=7#?
• What is the equation of the line normal to #f(x)=(5-x)^2 # at #x=2#?
• What is the equation of the line normal to #f(x)=(4-2x)^2 # at #x=-3#?
• What is the equation of the line normal to #f(x)=x^2 + sin(x) # at #x=pi#?
• What is the equation of the line normal to #f(x)= x^2sin^2(2x) # at #x=pi/6#?
• What is the equation of the line normal to #f(x)= xsin^2(2x) # at #x=pi/8#?
• What is the equation of the line normal to #f(x)=x ^3-3x^2 # at #x=4#?
• What is the equation of the line normal to #f(x)=x ^3-x^2 # at #x=-2#?
• What is the equation of the line normal to #f(x)=7x ^3+9x^2 # at #x=-2#?
• What is the equation of the line normal to #f(x)=x^2-3x # at #x=2#?
• What is the equation of the line normal to #f(x)=x^2-x # at #x=-2#?
• What is the equation of the line normal to #f(x)=2x^2-x+5 # at #x=-2#?
• What is the equation of the line normal to #f(x)=9x^2 - 28x - 34 # at #x=-1#?
• What is the equation of the line normal to #f(x)=9x^2 +2x - 4 # at #x=-1#?
• What is the equation of the line normal to #f(x)=-2x^2 +3x - 4 # at #x=-2#?
• What is the equation of the line normal to #f(x)=x^3-6x # at #x=2#?
• What is the equation of the line normal to #f(x)=x^3-6x^2-2 # at #x=1#?
• What is the equation of the line normal to #f(x)=6x^3+2x # at #x=3#?
• What is the equation of the line normal to #f(x)=2x^3 - x^2-x # at #x=4#?
• What is the equation of the line normal to #f(x)=x^3 - 7x^2-x # at #x=4#?
• What is the equation of the line normal to #f(x)=1/abs(x) # at #x=1#?
• What is the equation of the line normal to #f(x)=1/abs(x-6) # at #x=1#?
• What is the equation of the line normal to #f(x)=2x-x^2 # at #x=0#?
• What is the equation of the line normal to #f(x)=4x^2-7x+6 # at #x=1#?
• What is the equation of the line normal to #f(x)=6x^2 + 4x - 9 # at #x=1#?
• What is the equation of the line normal to #f(x)=6x^2 -x - 9 # at #x=1#?
• What is the equation of the line normal to #f(x)=x^2 -x +2 # at #x=1#?
• What is the equation of the line normal to #f(x)=3x^2 -x +1 # at #x=-3#?
• What is the equation of the line normal to #f(x)=3x^2 -5x +1 # at #x=-3#?
• What is the equation of the line normal to #f(x)=-4x^2 -5x +1 # at #x=-3#?
• What is the equation of the line normal to #f(x)= -1/x # at #x=-3#?
• What is the equation of the line normal to #f(x)= -1/(5-x^2) # at #x=-3#?
• What is the equation of the line normal to #f(x)= -1/(3-2x) # at #x=0#?
• What is the equation of the line normal to #f(x)= sqrt(3x^3-2x) # at #x=2#?
• What is the equation of the line normal to #f(x)= sqrt(2x^3-x) # at #x=1#?
• What is the equation of the line normal to #f(x)= -3x^5-8x^3+4x^2 # at #x=1#?
• What is the equation of the line normal to #f(x)= x^3+4x^2 # at #x=1#?
• What is the equation of the line normal to #f(x)=3x^2 - 12x-5 # at #x=1#?
• What is the equation of the line normal to #f(x)=3x^2 +x-5 # at #x=1#?
• What is the equation of the line normal to #f(x)=xe^x# at #x=7#?
• What is the equation of the line normal to #f(x)= x^3e^x # at #x=2#?
• What is the equation of the line normal to #f(x)= x^3/e^x # at #x=2#?
• What is the equation of the line normal to #f(x)= x^3-e^x # at #x=2#?
• What is the slope of the line normal to the tangent line of #f(x) = x^3-sqrtx # at # x= 3 #?
• What is the slope of the line normal to the tangent line of #f(x) = x^2-sqrtx # at # x= 3 #?
• What is the slope of the line normal to the tangent line of #f(x) = x^2-3sqrtx # at # x= 3 #?
• What is the slope of the line normal to the tangent line of #f(x) = 2x^2-3sqrt(x^2-x) # at # x= 12 #?
• What is the slope of the line normal to the tangent line of #f(x) = 2x^2-xsqrt(x^2-x) # at # x= 2 #?
• What is the slope of the line normal to the tangent line of #f(x) = 2x-xsqrt(x^2-1) # at # x= 2 #?
• What is the slope of the line normal to the tangent line of #f(x) = 2x-xsqrt(x-1) # at # x= 2 #?
• What is the slope of the line normal to the tangent line of #f(x) = 2x-4sqrt(x-1) # at # x= 2 #?
• What is the slope of the line normal to the tangent line of #f(x) = 2x-4/sqrt(x-1) # at # x= 2 #?
• What is the slope of the line normal to the tangent line of #f(x) = 2x-2 # at # x= 3 #?
• What is the slope of the line normal to the tangent line of #f(x) = sin(3x-pi) # at # x= pi/3 #?
• What is the slope of the line normal to the tangent line of #f(x) = sin(2x-pi/6) # at # x= pi/3 #?
• What is the slope of the line normal to the tangent line of #f(x) = cosx*sin(2x-pi/6) # at # x= pi/3 #?
• What is the slope of the line normal to the tangent line of #f(x) = cos(2x)*sin(2x-pi/12) # at # x= pi/3 #?
• What is the slope of the line normal to the tangent line of #f(x) = cosx+sin(2x-pi/12) # at # x= pi/3 #?
• What is the slope of the line normal to the tangent line of #f(x) = cosx+sin(2x-pi/12) # at # x= (5pi)/8 #?
• What is the slope of the line normal to the tangent line of #f(x) = tanx+sin(x-pi/4) # at # x= (5pi)/8 #?
• What is the slope of the line normal to the tangent line of #f(x) = tanx+sin(x-pi/4) # at # x= (5pi)/6 #?
• What is the slope of the line normal to the tangent line of #f(x) = cot^2x+sin(x-pi/4) # at # x= (5pi)/6 #?
• What is the slope of the line normal to the tangent line of #f(x) = cot^2x+sin(x-pi/2) # at # x= (5pi)/6 #?
• What is the slope of the line normal to the tangent line of #f(x) = secx+sin(2x-(3pi)/8) # at # x= (11pi)/8 #?
• What is the slope of the line normal to the tangent line of #f(x) = secx+sin(2x-(3pi)/8) # at # x= (11pi)/8 #?
• What is the slope of the line normal to the tangent line of #f(x) = sec^3x+sin(2x-(3pi)/8) # at # x= (11pi)/8 #?
• What is the slope of the line normal to the tangent line of #f(x) = cscx+sin(2x-(3pi)/8) # at # x= (11pi)/8 #?
• What is the slope of the line normal to the tangent line of #f(x) = cscx+cos^2(5x-pi) # at # x= (11pi)/8 #?
• What is the slope of the line normal to the tangent line of #f(x) = secx+cos^2(2x-pi) # at # x= (11pi)/8 #?
• What is the slope of the line normal to the tangent line of #f(x) = xe^-x # at # x= 0 #?
• What is the slope of the line normal to the tangent line of #f(x) = xe^-x+x^2-x # at # x= 0 #?
• What is the slope of the line normal to the tangent line of #f(x) = e^-x+x^2-x # at # x= 0 #?
• What is the slope of the line normal to the tangent line of #f(x) = e^(x-2)+x-2 # at # x= 0 #?
• What is the slope of the line normal to the tangent line of #f(x) = e^(x-2)+x-2 # at # x= 2 #?
• What is the slope of the line normal to the tangent line of #f(x) = e^(x-1)+x-2 # at # x= 2 #?
• What is the slope of the line normal to the tangent line of #f(x) = e^(x^2-1)+3x-2 # at # x= 1 #?
• What is the slope of the line normal to the tangent line of #f(x) = e^(x^2-1)+2x-2 # at # x= 1 #?
• What is the slope of the line normal to the tangent line of #f(x) = x^2e^(x-1)+2x-2 # at # x= 1 #?
• What is the slope of the line normal to the tangent line of #f(x) = x^2e^(x-1)+2x # at # x= 1 #?
• What is the slope of the line normal to the tangent line of #f(x) = xe^(x-1)+x^3 # at # x= 2 #?
• What is the slope of the line normal to the tangent line of #f(x) = xe^(x-3)+x^3 # at # x= 2 #?
• What is the slope of the line normal to the tangent line of #f(x) = e^(x-3)/x+x^3 # at # x= 2 #?
• What is the slope of the line normal to the tangent line of #f(x) = 1/x+x^3 # at # x= 2 #?
• What is the slope of the line normal to the tangent line of #f(x) = 1/(x^2-x+1) # at # x= 2 #?
• What is the slope of the line normal to the tangent line of #f(x) = 1/(x^2-2x+4) # at # x= 3 #?
• What is the slope of the line normal to the tangent line of #f(x) = x^3-4x # at # x= -1 #?
• What is the slope of the line normal to the tangent line of #f(x) = x-sqrt(x^2+4) # at # x= 2 #?
• What is the slope of the line normal to the tangent line of #f(x) = tanx-secx # at # x= (5pi)/12 #?
• What is the slope of the line normal to the tangent line of #f(x) = cscx-secx # at # x= (17pi)/12 #?
• What is the slope of the line normal to the tangent line of #f(x) = cscx-sec^2x +1 # at # x= (17pi)/12 #?
• What is the slope of the line normal to the tangent line of #f(x) = cosx-cos^2x +1 # at # x= (17pi)/12 #?
• What is the slope of the line normal to the tangent line of #f(x) = cscx-sin2x # at # x= (pi)/12 #?
• What is the slope of the line normal to the tangent line of #f(x) = sec^2x-sin^2x # at # x= (pi)/12 #?
• What is the slope of the line normal to the tangent line of #f(x) = secx-cos3x # at # x= (pi)/12 #?
• What is the slope of the line normal to the tangent line of #f(x) = secx-cos^2(x-pi) # at # x= (pi)/12 #?
• What is the slope of the line normal to the tangent line of #f(x) = xcotx-sin^2(x-pi) # at # x= (pi)/12 #?
• What is the slope of the line normal to the tangent line of #f(x) = xcotx+2xsin(x-pi/3) # at # x= (5pi)/8 #?
• What is the slope of the line normal to the tangent line of #f(x) = xcotx+2xsin(x-pi/3) # at # x= (15pi)/8 #?
• What is the slope of the line normal to the tangent line of #f(x) = xtanx-xsin(x-pi/3) # at # x= (15pi)/8 #?
• What is the slope of the line normal to the tangent line of #f(x) = xsecx-cos(2x-pi/6) # at # x= (15pi)/8 #?
• What is the slope of the line normal to the tangent line of #f(x) = sec^2x-xcos(x-pi/4) # at # x= (15pi)/8 #?
• What is the slope of the line normal to the tangent line of #f(x) = sec^2x-xcos(x-pi/4) # at # x= (7pi)/4 #?
• How to do this?
• How do you find the equation of the tangent and normal line to the curve #y=x^2-3# at (2,1)?
• How do you find the equation of the tangent and normal line to the curve #y=6-x^2# at (2,2)?
• How do you find the equation of the tangent and normal line to the curve #y=9x^-1# at x-3?
• How do you find the equation of the tangent and normal line to the curve #y=x^(1/2)# at x=1?
• How do you find the equation of the tangent and normal line to the curve #y=x^2# at x=-3?
• How do you find the equation of the tangent and normal line to the curve #y=x^2-x# at x=1?
• How do you find the equation of the tangent and normal line to the curve #y=x^3# at x=1?
• How do you find the equation of the tangent and normal line to the curve #y=1+x^(2/3)# at (0,1)?
• How do you find the equation of the tangent and normal line to the curve #y=1/x^3# at #(2,1/8)#?
• How do you find the equation of the tangent and normal line to the curve #y^3-3x-2y+6=0# at (9,3)?
• How do you find the equation of the tangent and normal line to the curve #y=x^3# at x=2?
• How do you find the equation of the tangent and normal line to the curve #y=x^2+2x+3# at x=1?
• How do you find the equation of the tangent and normal line to the curve #y=(x+1)/(x-3) at x=2?
• How do you find the equation of the tangent and normal line to the curve #y=sqrtx# at x=9?
• How do you find the equation of the tangent and normal line to the curve #y=1/x# at x=2?
• How do you find the equation of the tangent and normal line to the curve #y=e^x# at x=0?
• How do you find the equation of the tangent and normal line to the curve #y=lnx# at x=e?
• How do you find the equation of the tangent and normal line to the curve #y=lnx# at x=17?
• How do you find the equation of the tangent and normal line to the curve #y=sinx# at #x=pi/3#?
• How do you find the equation of the tangent and normal line to the curve #y=tanx# at #x=-pi/4#?
• How do you find the equation of the tangent and normal line to the curve #y=(2x+3)/(3x-2)# at #(1,5)#?
• How do you find the equation of the tangent and normal line to the curve #y=x+cosx# at #x=1#?
• What is the normal to the tangent line at the y-intercept to #y = 1/3x^3 - 4x + 2#?
• Question #680ff
• How do you find the equations for the normal line to #x^2+y^2=25# through (4,3)?
• How do you find the equations for the normal line to #x^2+y^2=9# through (0,3)?
• How do you find the equations for the normal line to #x^2/32+y^2/8=1# through (4,2)?
• How do you find the equations for the normal line to #x^2+y^2=20# through (2,4)?
• How do you find the equations for the normal line to #x^2-y^2=16# through (5,3)?
• How do you find the equations for the normal line to #y=x^2# through (2,4)?
• How do you find the equations for the normal line to #y=e^-x# through (0,0)?
• Question #b5ac6
• Question #05cf9
• Find the normal vector of the tangent plane to #x^2yz+3y^2-2xz^2+8z=0 # at #(1,2,-1)# ?