AP Calculus ABeasymcq1 pt

If f(x)>0f'(x)>0 on (,2)(3,)(-\infty,-2)\cup(3,\infty) and f(x)<0f'(x)<0 on (2,3)(-2,3), then ff has

A.a local minimum at x=2x=-2 and a local maximum at x=3x=3.
B.no local extrema.
C.a local minimum at both x=2x=-2 and x=3x=3.
D.a local maximum at x=2x=-2 and a local minimum at x=3x=3.

Explanation

Core Concept

ff' changes from positive to negative at x=2x=-2 (local maximum) and from negative to positive at x=3x=3 (local minimum).

Correct Answer

Da local maximum at x=2x=-2 and a local minimum at x=3x=3.

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