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

1 Answer
Nov 30, 2016

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

y=-3/2x

Explanation:

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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