For a differentiable

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

Problem

For a differentiable, invertible function

f

, suppose

(f^{-1})'(f(a))

exists. Which of the following must be true? (a)

(f^{-1})'(a)=0

(b)

f'(a)\neq 0

(c)

f'(f(a))\neq 0

(d)

f'(a)=0

Related theory

Derivatives of Inverse Functions
Advanced Differentiation
Derivatives of standard functions via chain rule
Derivatives of composite functions
Continuity and Differentiability

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