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What is the equation of the line tangent to #f(x)=-x^2 -2x - 1 # at #x=-1#?

Answer 1

The equation of the tangent line to #f# at the given point is #y=0# (the tangent line is the #x#-axis).

If #f(x)=-x^2-2x-1#, then #f'(x)=-2x-2# so that #f(-1)=-1+2-1=0# and #f'(-1)=2-2=0#.

In general, the equation of the tangent line to #f# at the point #(a,f(a))# is #y=f(a)+f'(a)(x-a)#. In the present case, this becomes

#y=f(-1)+f'(-1)(x+1)=0+0(x+1)=0#.

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Answer 2

Aurora Alvarado

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

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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.