Explain why the composite function can have a horizontal tangent at a point even when…

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

Problem

Explain why the composite function

h(x)=f\bigl(g(x)\bigr)

can have a horizontal tangent at a point even when

g'(x)\neq 0

at that point.

Related theory

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

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