How do you find the equation of the tangent to the curve #y = (4x + 8)/(x + 1)# which is parallel to #y = -4x + 7#?

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Answer 1 · 2018-04-02T11:49:16

#y=-4x+8#

If the equation of tangent is parallel to #y=-4x+7#, it has form of #y=-4x+k#

Also, tangent of it must be equal to derivative of #y=(4x+8)/(x+1)# curve

#(4*(x+1)-1*(4x+8))/(x+1)^2=-4#

#-4/(x+1)^2=-4#

#(x+1)^2=1#

#x^2+2x=0#

#x*(x+2)=0#

So, #x_1=-2# and #x_2=0#

For #x=-2#, #y=(4*(-2)+8)/(-2+1)=0/(-1)=0#

For #x=0#, #y=(4*0+8)/(0+1)=8/1=8#

According to equation of tangent formula,

#a)# #y-0=-4*(x-(-2))# or #y=-4x+8# for #(-2, 0)# point.

#b)# #y-8=-4*(x-0)# or #y=-4x+8# for #(0, -2)# point.