AP Calculus ABmediummcq1 pt

If f(3)=0f'(3)=0 and f(3)=2f''(3)=-2, which conclusion follows?

A.ff has a local minimum at x=3x=3.
B.ff has a point of inflection at x=3x=3.
C.ff has a local maximum at x=3x=3.
D.ff is increasing at x=3x=3.

Explanation

Core Concept

By the second derivative test, f(3)=0f'(3)=0 together with f(3)=2<0f''(3)=-2<0 means ff has a local maximum at x=3x=3.

Correct Answer

Cff has a local maximum at x=3x=3.

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