Let for all real

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let

f(x)=2x^{3}+3x

for all real

x

. The function

f

is invertible with inverse function

f^{-1}

. (a) Justify that

f

is invertible on

\mathbb{R}

. (b) Compute

f'(x)

. (c) Using your result from part (b), determine

(f^{-1})'(5)

Related theory

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

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