Apentix/AP Calculus AB/Unit 5: Analytical Applications of Differentiation/Question

AP Calculus ABmediummcq1 pt

Which statement about the graph of $f(x)=x^3-3x$ is true?

A.

f

has a local maximum at

(1,-2)

and a local minimum at

(-1,2)

.

B.

f

has no point of inflection.

C.

f

has a local maximum at

(-1,2)

, a local minimum at

(1,-2)

, and a point of inflection at

(0,0)

.

D.

f

is increasing on

(-1,1)

.

Explanation

Core Concept

$f'(x)=3x^2-3$ changes sign at $x=\pm1$ , giving $f(-1)=2$ (maximum) and $f(1)=-2$ (minimum). $f''(x)=6x$ changes sign at $x=0$ , so $(0,0)$ is a point of inflection.

Correct Answer

C $f$ has a local maximum at $(-1,2)$ , a local minimum at $(1,-2)$ , and a point of inflection at $(0,0)$ .

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