AP Calculus ABeasymcq1 pt

If $f'(x)>0$ for $x<c$ and $f'(x)<0$ for $x>c$ , then $f$ has a

A.local maximum at

x=c

B.local minimum at

x=c

C.point of inflection at

x=c

D.no local extremum at

x=c

Explanation

Core Concept

By the first derivative test, $f'$ changing from positive to negative at $c$ means $f$ rises to $c$ and falls after $c$ . So $f(c)$ is a local maximum.

Correct Answer

Alocal maximum at $x=c$ .

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If f′(x)>0f'(x)>0f′(x)>0 for x<cx<cx<c and f′(x)<0f'(x)<0f′(x)<0 for x>cx>cx>c, then fff has a

Explanation

Core Concept

Correct Answer

More Unit 5: Analytical Applications of Differentiation practice questions

If $f'(x)>0$ for $x<c$ and $f'(x)<0$ for $x>c$ , then $f$ has a