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

AP Calculus ABhardmcq1 pt

The graph of $f'$ is a line with positive slope that crosses the $x$ -axis at $x=2$ . Which statement about $f$ is true?

A.

f

has a local minimum at

x=2

and is concave up everywhere.

B.

f

has a local maximum at

x=2

and is concave up everywhere.

C.

f

has a local minimum at

x=2

and is concave down everywhere.

D.

f

has no local extremum at

x=2

.

Explanation

Core Concept

$f''$ equals the slope of the graph of $f'$ , a positive constant, so $f$ is concave up. $f'$ changes from negative to positive at $x=2$ , so $f$ has a local minimum there.

Correct Answer

A $f$ has a local minimum at $x=2$ and is concave up everywhere.

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