AP

MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

f(x)=x^{4}-4x^{3}+4x^{2}+1

. (i) Solve

f'(x)=0

and list all stationary points. (ii) Using the second derivative, decide whether each stationary point is a local maximum or a local minimum. (iii) Arrange the stationary points in ascending order of their corresponding function values, clearly marking each as a maximum or a minimum.

Related theory

Differentiation Rules
Curve Analysis
Maxima and minima

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