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

AP Calculus ABmediummcq1 pt

Suppose $f'(x)<0$ on $(-\infty,1)$ , $f'(x)>0$ on $(1,\infty)$ , and $f''(x)>0$ for all $x$ . Which statement describes the graph of $f$ ?

A.

f

is decreasing for

x<1

and increasing for

x>1

, concave up everywhere, with a local minimum at

x=1

.

B.

f

is increasing for

x<1

and decreasing for

x>1

, concave up everywhere, with a local maximum at

x=1

.

C.

f

is decreasing for

x<1

and increasing for

x>1

, concave down everywhere.

D.

f

is decreasing for all

x

with a point of inflection at

x=1

.

Explanation

Core Concept

$f'$ changes from negative to positive at $x=1$ , giving a local minimum, and $f''>0$ everywhere makes the graph concave up.

Correct Answer

A $f$ is decreasing for $x<1$ and increasing for $x>1$ , concave up everywhere, with a local minimum at $x=1$ .

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