Consider the function on the interval

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

Problem

Consider the function

f(x)=k\sin x+m x

on the interval

\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]

, where

k

and

m

are constants. Given that

f(0)=0,\quad (f^{-1})'(0)=\dfrac{1}{4},\quad \text{and}\quad f\!\left(\dfrac{\pi}{2}\right)=3,

determine the values of

k

and

m

Related theory

Differentiation Rules
Derivatives of Inverse Functions
Advanced Differentiation

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