Consider the function

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

Problem

f(x)=k x^{3}

, where

k\neq 0

. Given that

(f^{-1})'(8)=\dfrac{1}{12}

, determine the value of

k

. (a)

\displaystyle k=\dfrac{1}{16}

(b)

\displaystyle k=16

(c)

\displaystyle k=1

(d)

\displaystyle k=8

Related theory

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

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