Let be differentiable and strictly increasing on an interval containing and

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

Problem

Let

f

be differentiable and strictly increasing on an interval containing

x=1

and

x=4

. Suppose

f(1)=3

with

f'(1)=0.5

and

f(4)=8

with

f'(4)=2.1

. Let

g=f^{-1}

. Calculate

g'(3)

and

g'(8)

, then indicate which of the two slopes has the greater magnitude.

Related theory

Derivatives of Inverse Functions
Advanced Differentiation
Functions
Implicit and Parametric Differentiation
Derivatives of inverse trigonometric functions
Continuity and Differentiability

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