A differentiable function satisfies with and where the tangent to the graph is…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

A differentiable function ff satisfies f(0)=2f(0)=2 with f′(0)=0f'(0)=0 and f(−1)=0f(-1)=0 where the tangent to the graph is vertical (so f′f' is undefined at x=−1x=-1). For g=f−1g=f^{-1}, determine (a) g′(2)g'(2) (b) whether g′(0)g'(0) exists, and if so, its value.

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