What is the equation of the tangent line of #f(x)=3/(2x+4) # at #x=-1#?

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Answer 1 · 2016-11-30T13:55:57

The tangent line of #f(x)= frac3 (2x+4)# at #x=-1# is

#y=-3/2x#

The general formula for the tangent line of the graph of a continuous function is:

#y = f(x_0)+f'(x_0)(x-x_0)#

calculate the derivative of #f(x)#:

#f'(x)=d/(dx) (frac3 (2x+4))= -frac 6 ((2x+4)^2)#

Pose #x_0=-1#

#f(x_0)=frac3 (2(-1)+4)=3/2#

#f'(x_0)=-frac 6 ((2(-1)+4)^2)=-3/2#

And the tangent line is:

#y=3/2-3/2(x+1)=-3/2x#

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