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

Answer 1

Cameron Alexander

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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Answer 2

Isaiah Allen

The equation of the tangent line of f(x)=3/(2x+4) at x=-1 is y = -3/2(x+1) - 3/4.

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Answer 3

Scarlett Allison

The equation of the tangent line of f(x) = 3/(2x + 4) at x = -1 is y = 3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.