The function is defined by

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

Problem

The function

g

is defined by

g(x)=k x^{2}+c

, where

k>0

and

c

are constants. It is known that

(g^{-1})'(8)=\dfrac{1}{6}

and

(g^{-1})'(53)=\dfrac{1}{24}

. What is the ordered pair

(k,c)

? (a)

(5,3)

(b)

(3,5)

(c)

(12,5)

(d)

(2,4)

Related theory

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

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