Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)

Key Questions

• How do you know a function is increasing?

  Answer:

  It will be increasing when the first derivative is positive.

  Explanation:

  Take the example of the function #f(x) = e^(x^2 - 1)#.

  The first derivative is given by #f'(x) = 2xe^(x^2 - 1)# (chain rule). We see that the derivative will go from increasing to decreasing or vice versa when #f'(x) = 0#, or when #x= 0#.

  Whenever you have a positive value of #x#, the derivative will be positive, therefore the function will be increasing on #{x|x> 0, x in RR}#.

  The graph confirms

  

  Hopefully this helps!

  Noah G · 1 · Mar 9 2018
• What is the meaning of monotonically increasing function?

  Answer:

  If #x_0 < x_1# then #f(x_0) < f(x_1)#

  Explanation:

  The meaning is that you have a function with positive slope in every point of Dom.

  Starting from a #x_0# and move to right, the graph of function is moving up at the same time

  F. Javier B. · 1 · May 24 2018

• How do you know a function is increasing?
• What is the meaning of monotonically increasing function?
• How do you find all intervals where the function #f(x)=1/3x^3+3/2x^2+2# is increasing?
• How do you find all intervals where the function #f(x)=e^(x^2)# is increasing?
• What is the derivative graph of a parabola?
• If #f(x) = 2x^3 + 3x^2 - 180x#, how do I find the intervals on which f is increasing and decreasing?
• Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?
• What information does the first derivative tell you?
• How do you find the interval in which the function #f(x)=2x^3 + 3x^2+180x# is increasing or decreasing?
• How do you find values of t in which the speed of the particle is increasing if he position of a particle moving along a line is given by #s(t)=2t^3-24t^2+90t+7# for #t≥0#?
• How do you know a function is decreasing or increasing at #x=1# given the function #4x^2-9x#?
• Is #f(x)=x^2-x# increasing or decreasing at #x=1#?
• Is #f(x)=x^2(x-2)-3x# increasing or decreasing at #x=1#?
• Is #f(x)=1/(x-1)-1/(x+1)^2# increasing or decreasing at #x=0#?
• Is #f(x)=x-sqrt(x^3-3x)# increasing or decreasing at #x=2#?
• Is #f(x)=x-1/sqrt(x^3-3x)# increasing or decreasing at #x=2#?
• Is #f(x)=3x^2-x+4# increasing or decreasing at #x=2#?
• Is #f(x)=-4x^2+x-1# increasing or decreasing at #x=1#?
• Is #f(x)=-x^2+3x-1# increasing or decreasing at #x=1#?
• Is #f(x)=-2x^2-2x-1# increasing or decreasing at #x=-1#?
• Is #f(x)=-x^3+3x^2-x+2# increasing or decreasing at #x=-1#?
• Is #f(x)=-2x^3+2x^2-x+2# increasing or decreasing at #x=0#?
• Is #f(x)=-2x^3+4x^2-3x-1# increasing or decreasing at #x=0#?
• Is #f(x)=-7x^3+x^2-2x-1# increasing or decreasing at #x=-2#?
• Is #f(x)=-3x^3-5x^2-x-1# increasing or decreasing at #x=-2#?
• Is #f(x)=-x^3-2x^2-3x-1# increasing or decreasing at #x=2#?
• Is #f(x)=-4x^3+4x^2+2x-1# increasing or decreasing at #x=2#?
• Is #f(x)=-4x^3+x^2+2x+2# increasing or decreasing at #x=2#?
• Is #f(x)=-12x^3+17x^2+2x+2# increasing or decreasing at #x=2#?
• Is #f(x)=-2x^3-5x^2-6x-1# increasing or decreasing at #x=1#?
• Is #f(x)=(x-3)(x+3)(x-2)# increasing or decreasing at #x=1#?
• Is #f(x)=(x-3)(x+3)(x-2)# increasing or decreasing at #x=3#?
• Is #f(x)=(x+2)(2x-3)(x-2)# increasing or decreasing at #x=0#?
• Is #f(x)=(x+1)(2x-3)(3x-2)# increasing or decreasing at #x=0#?
• Is #f(x)=(x+1)(x+2)(x-2)# increasing or decreasing at #x=0#?
• Is #f(x)=(x+3)(x-2)(x+4)# increasing or decreasing at #x=-1#?
• Is #f(x)=(x+3)(x-2)(x-2)# increasing or decreasing at #x=-2#?
• Is #f(x)=(2x+3)(x-6)(x-2)# increasing or decreasing at #x=-2#?
• Is #f(x)=(x+3)(x-6)(x/3-1)# increasing or decreasing at #x=-2#?
• Is #f(x)=(x+7)(x-2)(x-1)# increasing or decreasing at #x=-1#?
• Is #f(x)=(x-4)(x-12)(x/4-1)# increasing or decreasing at #x=-1#?
• Is #f(x)=(x-16)(x-12)(x/4+3)# increasing or decreasing at #x=1#?
• Is #f(x)=(x-1)(x-1)(x-3)# increasing or decreasing at #x=1#?
• Is #f(x)=(x+3)(x-8)(x-3)# increasing or decreasing at #x=1#?
• Is #f(x)=(x+1)(x-4)(x-2)# increasing or decreasing at #x=1#?
• Is #f(x)=(x+1)(x+5)(x-7)# increasing or decreasing at #x=-1#?
• Is #f(x)=(x-3)(x+11)(x-7)# increasing or decreasing at #x=-1#?
• Is #f(x)=(x-3)(x+15)(x+2)# increasing or decreasing at #x=-1#?
• Is #f(x)=(x-3)(x+5)(x+2)# increasing or decreasing at #x=-3#?
• Is #f(x)=(x-2)(x+5)(x+2)# increasing or decreasing at #x=-3#?
• Is #f(x)=(x-2)(x+5)(x-1)# increasing or decreasing at #x=-1#?
• Is #f(x)=(x-2)(2x-3)(2x-1)# increasing or decreasing at #x=-2#?
• Is #f(x)=(x-1)(x-3)(2x-1)# increasing or decreasing at #x=2#?
• Is #f(x)=(x+3)(x-3)(3x-1)# increasing or decreasing at #x=2#?
• Is #f(x)=(x-2)(x+1)(x+4)# increasing or decreasing at #x=1#?
• Is #f(x)=(2x-2)(x+1)(x+4)# increasing or decreasing at #x=-1#?
• Is #f(x)=(2x-2)(x+1)(x+4)# increasing or decreasing at #x=1#?
• Is #f(x)=(x-2)^2(x+1)(x+4)# increasing or decreasing at #x=1#?
• Is #f(x)=(x-2)^2(x+1)# increasing or decreasing at #x=1#?
• Is #f(x)=(x-2)^2(x-1)# increasing or decreasing at #x=1#?
• Is #f(x)=(x-2)^2/(x-1)# increasing or decreasing at #x=2#?
• Is #f(x)=(x-2)^2/(x+1)# increasing or decreasing at #x=2#?
• Is #f(x)=(x^2-2)/(x-1)# increasing or decreasing at #x=2#?
• Is #f(x)=(x^2-2)/(x+1)# increasing or decreasing at #x=1#?
• Is #f(x)=(x^2-3x-2)/(x+1)# increasing or decreasing at #x=1#?
• Is #f(x)=(x^2-3x-2)/(x^2+1)# increasing or decreasing at #x=1#?
• Is #f(x)=(x^2-4x-2)/(x^2+1)# increasing or decreasing at #x=-3#?
• Is #f(x)=(-2x^2-4x-2)/(2x^2+1)# increasing or decreasing at #x=-3#?
• Is #f(x)=(-x^2-5x-2)/(x^2+1)# increasing or decreasing at #x=-3#?
• Is #f(x)=(-x^2+5x-2)/(x^2-1)# increasing or decreasing at #x=-3#?
• Is #f(x)=(-x^2+3x+2)/(x^2-1)# increasing or decreasing at #x=2#?
• Is #f(x)=(-3x^2-3x+2)/(x^2+3)# increasing or decreasing at #x=1#?
• Is #f(x)=(-3x^2-3x-2)/(x^2+x)# increasing or decreasing at #x=1#?
• Is #f(x)=(-3x^2-x+2)/(x^2+x)# increasing or decreasing at #x=1#?
• Is #f(x)=(-x^3-2x^2-x+2)/(x^2+x)# increasing or decreasing at #x=1#?
• Is #f(x)=(-x^3-x^2-x+2)/(x^2+3x)# increasing or decreasing at #x=1#?
• Is #f(x)=(-7x^3-x^2-2x+2)/(x^2+3x)# increasing or decreasing at #x=1#?
• Is #f(x)=(-5x^3-x^2+2x-2)/(-x+3)# increasing or decreasing at #x=1#?
• Is #f(x)=(-2x^3+4x^2-x-2)/(x+3)# increasing or decreasing at #x=-2#?
• Is #f(x)=(x^3+2x^2-x-2)/(x+3)# increasing or decreasing at #x=-2#?
• Is #f(x)=(x^3+3x^2-x-9)/(x+1)# increasing or decreasing at #x=-2#?
• Is #f(x)=(x^3+3x^2-4x-9)/(x+1)# increasing or decreasing at #x=0#?
• Is #f(x)=(x^3-6x^2-4x-9)/(x+1)# increasing or decreasing at #x=0#?
• Is #f(x)=(x^2-4x-9)/(x+1)# increasing or decreasing at #x=0#?
• Is #f(x)=(x^2-5x-9)/(2x+1)# increasing or decreasing at #x=0#?
• Is #f(x)=(x^2+2x-6)/(2x+1)# increasing or decreasing at #x=0#?
• Is #f(x)=(x^2+2x-2)/(2x-4)# increasing or decreasing at #x=0#?
• Is #f(x)=(-2x^2-5x-2)/(2x-4)# increasing or decreasing at #x=0#?
• Is #f(x)=(-2x^2-15x-12)/(2x-4)# increasing or decreasing at #x=0#?
• Is #f(x)=(-12x^2-22x-2)/(x-4)# increasing or decreasing at #x=1#?
• Is #f(x)=(-x^2-2x-2)/(x-3)# increasing or decreasing at #x=1#?
• Is #f(x)=(x^2-6x-12)/(x+2)# increasing or decreasing at #x=1#?
• Is #f(x)=(12x^2-16x-12)/(x+2)# increasing or decreasing at #x=5#?
• Is #f(x)=(6x^2-x-12)/(x+3)# increasing or decreasing at #x=3#?
• Is #f(x)=(x^3-4x^2-4x+5)/(x+2)# increasing or decreasing at #x=3#?
• Is #f(x)=(3x^3-2x^2-2x+5)/(x+2)# increasing or decreasing at #x=3#?
• Is #f(x)=(-x^3-2x^2-12x+2)/(x-4)# increasing or decreasing at #x=3#?
• Is #f(x)=(-x^3-7x^2-x+2)/(x-2)# increasing or decreasing at #x=3#?
• Is #f(x)=(3x^3+3x^2+5x+2)/(x-2)# increasing or decreasing at #x=3#?
• Is #f(x)=(3x^3+x^2-2x+7)/(2x-2)# increasing or decreasing at #x=3#?
• Is #f(x)=(-x^3+x^2-x+7)/(x-2)# increasing or decreasing at #x=-1#?
• Is #f(x)=(-x^3+2x^2-3x+7)/(x-2)# increasing or decreasing at #x=-1#?
• Is #f(x)=(4x^3+2x^2-2x-3)/(x-2)# increasing or decreasing at #x=-1#?
• Is #f(x)=(4x^3-2x^2-x-3)/(x-2)# increasing or decreasing at #x=0#?
• Is #f(x)=(x^3-2x^2+5x-4)/(x-2)# increasing or decreasing at #x=0#?
• Is #f(x)=(x^3+7x^2-5x-4)/(x-2)# increasing or decreasing at #x=0#?
• Is #f(x)=(x^3-4x^2+3x-4)/(4x-2)# increasing or decreasing at #x=0#?
• Is #f(x)=(-2x^3+3x^2+3x-4)/(4x-2)# increasing or decreasing at #x=0#?
• Is #f(x)=(-2x^3+x^2-2x-4)/(4x-2)# increasing or decreasing at #x=0#?
• Is #f(x)=(x^3+x^2+2x-4)/(4x-2)# increasing or decreasing at #x=0#?
• Is #f(x)=(-x^3+x^2-3x-4)/(4x-2)# increasing or decreasing at #x=0#?
• Is #f(x)=(-x^3+x^2-5x+6)/(x-2)# increasing or decreasing at #x=0#?
• Is #f(x)=(-2x^3+9x^2-5x+6)/(x-2)# increasing or decreasing at #x=0#?
• Is #f(x)=(-2x^3-6x^2-3x+2)/(2x-1)# increasing or decreasing at #x=0#?
• Is #f(x)=(x^3-5x^2-x+2)/(2x-1)# increasing or decreasing at #x=0#?
• Is #f(x)=(x^3-3x^2-5x+2)/(x+1)# increasing or decreasing at #x=0#?
• Is #f(x)=(-2x^3-x^2-5x+2)/(x+1)# increasing or decreasing at #x=0#?
• Is #f(x)=(-x^3-x^2+2x+2)/(x+1)# increasing or decreasing at #x=0#?
• Is #f(x)=(x^3-9x^2+12x+2)/(x+1)# increasing or decreasing at #x=0#?
• Is #f(x)=(x^3+5x^2-7x+2)/(x+1)# increasing or decreasing at #x=0#?
• Is #f(x)=(4x^3+5x^2-2x+7)/(x+1)# increasing or decreasing at #x=0#?
• Is #f(x)=(2x^3+5x^2-9x+1)/(x-4)# increasing or decreasing at #x=0#?
• Is #f(x)=(-3x^3+15x^2-2x+1)/(x-4)# increasing or decreasing at #x=2#?
• Is #f(x)=(2x^3+2x^2+2x+1)/(x-3)# increasing or decreasing at #x=2#?
• Is #f(x)=(2x^3-7x^2+3x+1)/(x-3)# increasing or decreasing at #x=2#?
• Is #f(x)=(2x^3-7x^2+13x-11)/(x-3)# increasing or decreasing at #x=2#?
• Is #f(x)=(3x^3-5x^2+13x-11)/(x-3)# increasing or decreasing at #x=2#?
• Is #f(x)=(-5x^3-x^2-3x-11)/(x-3)# increasing or decreasing at #x=2#?
• Is #f(x)=(-5x^3+x^2-3x-11)/(x-1)# increasing or decreasing at #x=2#?
• Is #f(x)=(-x^3+x^2+2x-11)/(x-1)# increasing or decreasing at #x=2#?
• Is #f(x)=(3x^3+x^2-2x-14)/(x-1)# increasing or decreasing at #x=2#?
• Is #f(x)=(x^3-4x^2-2x-4)/(x-1)# increasing or decreasing at #x=2#?
• Is #f(x)=1/e^x# increasing or decreasing at #x=0#?
• Is #f(x)=xe^x# increasing or decreasing at #x=0#?
• Is #f(x)=x/(2-e^x)# increasing or decreasing at #x=0#?
• Is #f(x)=x^2lnx# increasing or decreasing at #x=1#?
• Is #f(x)=x^2-3lnx# increasing or decreasing at #x=1#?
• Is #f(x)=x/(x+x^2)-lnx# increasing or decreasing at #x=1#?
• Is #f(x)=x(lnx)^2# increasing or decreasing at #x=1#?
• Is #f(x)=xln(x)^2# increasing or decreasing at #x=1#?
• Is #f(x)=sqrt(ln(x)^2)# increasing or decreasing at #x=1#?
• Is #f(x)=e^x(x^2-x)# increasing or decreasing at #x=3#?
• Is #f(x)=e^xsqrt(x^2-x)# increasing or decreasing at #x=3#?
• Is #f(x)=e^x/sqrt(x^2-x)# increasing or decreasing at #x=3#?
• Is #f(x)=e^(x^2-x)-x^2# increasing or decreasing at #x=3#?
• Is #f(x)=e^(x^2-x)(x^2-x)# increasing or decreasing at #x=2#?
• Is #f(x)=e^(x^2-x)/(x^2-x)# increasing or decreasing at #x=2#?
• Is #f(x)=(1-e^x)/x^2# increasing or decreasing at #x=2#?
• Is #f(x)=(1-e^x)/(1-x^2)# increasing or decreasing at #x=2#?
• Is #f(x)=(1-xe^x)/(1-x^2)# increasing or decreasing at #x=2#?
• Is #f(x)=(x-e^x)/(x-x^2)# increasing or decreasing at #x=2#?
• Is #f(x)=(x-xe^x)/(x-1)# increasing or decreasing at #x=2#?
• Is #f(x)=(x-e^x)/(x-1)^3# increasing or decreasing at #x=2#?
• Is #f(x)=e^x/(x-2)# increasing or decreasing at #x=3#?
• Is #f(x)=(x^2e^x)/(x+2)# increasing or decreasing at #x=-1#?
• Is #f(x)=(x^2-e^x)/(x-2)# increasing or decreasing at #x=-1#?
• Is #f(x)=sinx-cosx# increasing or decreasing at #x=0#?
• Is #f(x)=cos(-x)# increasing or decreasing at #x=0#?
• Is #f(x)=tanx# increasing or decreasing at #x=0#?
• Is #f(x)=tanx-sinx# increasing or decreasing at #x=pi/3#?
• Is #f(x)=cosx*sinx# increasing or decreasing at #x=pi/3#?
• Is #f(x)=cscx-sinx# increasing or decreasing at #x=pi/3#?
• Is #f(x)=x-e^xsinx# increasing or decreasing at #x=pi/3#?
• Is #f(x)=x-e^x/sinx# increasing or decreasing at #x=pi/3#?
• Is #f(x)=sinx/x# increasing or decreasing at #x=pi/3#?
• Is #f(x)=sinx/e^x# increasing or decreasing at #x=pi/3#?
• Is #f(x)=cosx/e^x# increasing or decreasing at #x=pi/6#?
• Is #f(x)=cosx/(pi-e^x)# increasing or decreasing at #x=pi/6#?
• Is #f(x)=e^-xcos(-x)-sinx/(pi-e^x)# increasing or decreasing at #x=pi/6#?
• Is #f(x)=e^-xcos(-x)# increasing or decreasing at #x=pi/6#?
• Is #f(x)=cosx+sinx# increasing or decreasing at #x=pi/6#?
• Is #f(x)=cos^2x+sin2x# increasing or decreasing at #x=pi/6#?
• Is #f(x)=cos2x-sin^2x# increasing or decreasing at #x=pi/6#?
• Is #f(x)=cotx-e^xtanx# increasing or decreasing at #x=pi/6#?
• Is #f(x)=e^x+cosx^2# increasing or decreasing at #x=pi/6#?
• Is #f(x)=e^x+cosx-e^xsinx# increasing or decreasing at #x=pi/6#?
• Is #f(x)=e^x/cosx-e^x/sinx# increasing or decreasing at #x=pi/6#?
• Is #f(x)=cosx*tanx-sinx# increasing or decreasing at #x=pi/6#?
• Is #f(x)=cosx+tanx-sinx# increasing or decreasing at #x=pi/6#?
• Is #f(x)=cosx+cotx*sinx# increasing or decreasing at #x=pi/6#?
• Is #f(x)=cot(2x)*tanx# increasing or decreasing at #x=pi/6#?
• Is #f(x)=cot(2x)*tanx^2# increasing or decreasing at #x=pi/3#?
• Is #f(x)=cotx*tanx# increasing or decreasing at #x=pi/3#?
• Is #f(x)=sinx-cos(pi-x)# increasing or decreasing at #x=pi/3#?
• Is #f(x)=sin(pi/2-x)-cos(pi-x)# increasing or decreasing at #x=pi/3#?
• Is #f(x)=sin(3x)-cos(2x-pi)# increasing or decreasing at #x=pi/3#?
• Is #f(x)=xe^(x^3-x)-x^3# increasing or decreasing at #x=4#?
• Is #f(x)=xe^(x^3-x)-1/x^3# increasing or decreasing at #x=4#?
• Is #f(x)=x-e^(2x)-1/x^2# increasing or decreasing at #x=2#?
• Is #f(x)=1/x-1/x^3+1/x^5# increasing or decreasing at #x=2#?
• Is #f(x)=1/x-1/x^3+1/x^5# increasing or decreasing at #x=1#?
• Is #f(x)=1/x-1/x^3+1/x^5# increasing or decreasing at #x=-1#?
• Is #f(x)=(1-x)/(x+2)^3# increasing or decreasing at #x=-1#?
• Is #f(x)=(3-e^(2x))/x# increasing or decreasing at #x=-1#?
• Is #f(x)=(1-e^(2x))/(2x-4)# increasing or decreasing at #x=-1#?
• Is #f(x)=(1-e^(2/x))/(2x-4)# increasing or decreasing at #x=-1#?
• Is #f(x)=ln(2x^2-1)# increasing or decreasing at #x=-1#?
• Is #f(x)=-xln(2x^2)# increasing or decreasing at #x=-1#?
• Is #f(x)=-x/(x-5)# increasing or decreasing at #x=-1#?
• Is #f(x)=x^3-2x+4 # increasing or decreasing at #x=0 #?
• Is #f(x)=x^3+2x-4 # increasing or decreasing at #x=0 #?
• Is #f(x)=-2x^2-3x+4 # increasing or decreasing at #x=-2 #?
• Is #f(x)=x^2-3x # increasing or decreasing at #x=-2 #?
• Is #f(x)=e^x-3x # increasing or decreasing at #x=-1 #?
• Is #f(x)=xe^x-3x # increasing or decreasing at #x=-3 #?
• Is #f(x)=xe^x-x^2e^x # increasing or decreasing at #x=0 #?
• Is #f(x)=x^2e^x # increasing or decreasing at #x=1 #?
• Is #f(x)=e^x # increasing or decreasing at #x=1 #?
• Is #f(x)=x/e^x # increasing or decreasing at #x=1 #?
• Is #f(x)=(x-2)/e^x # increasing or decreasing at #x=-2 #?
• Is #f(x)=(x-2)e^x # increasing or decreasing at #x=-2 #?
• Is #f(x)=4xe^x # increasing or decreasing at #x=-2 #?
• Is #f(x)=4x-e^(3x-2) # increasing or decreasing at #x=-2 #?
• Is #f(x)=4x-e^(x+2) # increasing or decreasing at #x=-1 #?
• Is #f(x)=-e^(x^2+2) # increasing or decreasing at #x=0 #?
• Is #f(x)=-e^(x^2-3x+2) # increasing or decreasing at #x=0 #?
• Is #f(x)=-x/e^(x^2-3x+2) # increasing or decreasing at #x=4 #?
• Is #f(x)=sqrt(x+2) # increasing or decreasing at #x=2 #?
• Is #f(x)=sqrt(1/x-2) # increasing or decreasing at #x=2 /9 #?
• Is #f(x)=1/sqrt(x+3) # increasing or decreasing at #x=3 #?
• Is #f(x)=x/sqrt(x+3) # increasing or decreasing at #x=5 #?
• Is #f(x)=(x-3)/sqrt(x+3) # increasing or decreasing at #x=5 #?
• Is #f(x)=(x-3)/sqrt(x+3) # increasing or decreasing at #x=3 #?
• Is #f(x)=sqrt(xe^x+3x) # increasing or decreasing at #x=0 #?
• Is #f(x)=3x^3-2x^2 # increasing or decreasing at #x=0 #?
• Is #f(x)=3x^3-6x-7 # increasing or decreasing at #x=0 #?
• Is #f(x)=(x-2)^2-6x-7 # increasing or decreasing at #x=-2 #?
• Is #f(x)=(2x+4)^2-6x-7 # increasing or decreasing at #x=-2 #?
• Is #f(x)=(x+4)^2+x^2-3x # increasing or decreasing at #x=-2 #?
• Is #f(x)=(-x-4)^2+3x^2-3x # increasing or decreasing at #x=-1 #?
• Is #f(x)=(x-1)^2+2x^2-3x # increasing or decreasing at #x=-1 #?
• Is #f(x)=(x+2)^2-4x^2-3x # increasing or decreasing at #x=-1 #?
• Is #f(x)=(x+3)^3-4x^2-2x # increasing or decreasing at #x=0 #?
• Is #f(x)=(x-3)^3+3x^2-2x # increasing or decreasing at #x=0 #?
• Is #f(x)= 2xsinx # increasing or decreasing at #x=pi/3 #?
• Is #f(x)= x/sinx # increasing or decreasing at #x=-pi/6 #?
• Is #f(x)= x-12sinx # increasing or decreasing at #x=-pi/6 #?
• Is #f(x)= x-12sin(3x-pi/4) # increasing or decreasing at #x=-pi/6 #?
• Is #f(x)= x/pi-2sin(3x-pi/4) # increasing or decreasing at #x=-pi/6 #?
• Is #f(x)= cos(3x-pi/6)+2sin(4x-(3pi)/4) # increasing or decreasing at #x=pi/12 #?
• Is #f(x)=5 cos(3x+(5pi)/6)+ 2sin(4x-(3pi)/4) # increasing or decreasing at #x=pi/12 #?
• Is #f(x)= 4sin(4x-(3pi)/4) # increasing or decreasing at #x=pi/12 #?
• Is #f(x)= 4sin(4x-(3pi)/8) # increasing or decreasing at #x=pi/12 #?
• Is #f(x)= sin(x+(3pi)/8) # increasing or decreasing at #x=pi/12 #?
• Is #f(x)= cot(3x+(3pi)/8) # increasing or decreasing at #x=pi/12 #?
• Is #f(x)= cot(3x+(5pi)/8) # increasing or decreasing at #x=pi/4 #?
• Is #f(x)= cot(-x+(5pi)/6) # increasing or decreasing at #x=pi/4 #?
• Is #f(x)= cos(x+(5pi)/6) # increasing or decreasing at #x=pi/4 #?
• Is #f(x)= cos(x+(5pi)/4) # increasing or decreasing at #x=-pi/4 #?
• Is #f(x)= cos(3x+(5pi)/4) # increasing or decreasing at #x=-pi/4 #?
• Is #f(x)= 4xcos(3x-(5pi)/4) # increasing or decreasing at #x=-pi/4 #?
• Is #f(x)= cos(2x+(3pi)/4) # increasing or decreasing at #x=-pi/4 #?
• Is #f(x)= cos(x+(pi)/4) # increasing or decreasing at #x=pi/3 #?
• If #f(x)=sinx-xcosx#, how the function behaves in the intervals #(0,pi)# and #(pi,2pi)# i.e. whether it is increasing or decreasing?
• What interval(s) is #x / (1+x)^2 # increasing and decreasing?
• How do you find the absolute maximum and absolute minimum values of f on the given interval: #f(t) =t sqrt(25-t^2)# on [-1, 5]?
• How do you find the absolute maximum and absolute minimum values of f on the given interval: #f(x) = x-ln(3x) # on [0.5, 2]?
• How do you find the intervals of increasing and decreasing given #y=-x^3+2x^2+2#?
• How do you find the intervals of increasing and decreasing given #y=x^3-11x^2+39x-47#?
• How do you find the intervals of increasing and decreasing given #y=-x^4+3x^2-3#?
• How do you find the intervals of increasing and decreasing given #y=x^2/(4x+4)#?
• How do you find the intervals of increasing and decreasing given #y=(3x^2-3)/x^3#?
• How do you find the intervals of increasing and decreasing given #y=(2x-8)^(2/3)#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=x^2-6x+8#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=x^4-2x^2#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=1/(x+1)^2#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=x^2-2x-8#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=xsqrt(16-x^2)#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=x+4/x#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=x-2cosx#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=x^2-4x#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=x^2+6x+10#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=-2x^2+4x+3#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=-(x^2+8x+12)#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=2x^3+3x^2-12x#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=(x-1)^2(x+3)#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=(x+2)^2(x-1)#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=(x^5-5x)/5#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=x^4-32x+4#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=x^(2/3)-4#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=(x+2)^(2/3)#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=(x-1)^(1/3)#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=5-abs(x-5)#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=abs(x+4)-1#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=2x+1/x#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=(x+4)/x^2#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=x/2+cosx#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=sinx+cosx#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=cos^2(2x)#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=sin^2x+sinx# in #0 ≤ x ≤ (5pi)/2#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=2xsqrt(9-x^2)#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=10(5-sqrt(x^2-3x+16))#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=(x^5-4x^3+3x)/(x^2-1)#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=x(x^2-3)#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=cos^2x-sin^2x#?
• How do you find the intervals of increasing and decreasing using the first derivative given #y=x^3-4x#?
• Question #c66f7
• How do you find the largest open interval where the function is decreasing #f(x)=sqrt(4-x)#?
• Question #932f1
• Question #f729c
• How to prove that (tan b / tab a) > (b/a) whenever 0 < a < b < π/2?
• Question #0f52d
• Question #ed9fd
• (a) Find the interval on which f is increasing and decreasing? (b) Find the local maximum value of f? (c) Find the inflection point? (d) Find the interval on which f is concave up and concave down?
• How to demonstrate that #sqrt(2)^(sqrt(3)-1)>sqrt(3)^(sqrt(2)-1)#?We know that #g:(1,+oo)->RR,g(x)=##(lnx)/(x-1)#,and #g# is decreasing.
• In which interval the function #f(x)=sqrt(x^2+8)-x# is a decreasing function?
• What is the end behaviour of #y = -x^4#?
• Only one option is correct ,Please help ; How to solve this question?
• Another question involving functions and derivates. I solved a third of it but the other two parts are confusing. Can someone help me solve it?