AP Calculus ABeasymcq1 pt

If f(c)=0f'(c) = 0 and f(c)<0f''(c) < 0, which of the following must be true about the function ff at x=cx = c?

A.ff has an absolute maximum at x=cx = c.
B.ff has a relative minimum at x=cx = c.
C.ff has a relative maximum at x=cx = c.
D.ff has a point of inflection at x=cx = c.

Explanation

Core Concept

Correct. The Second Derivative Test states that if f(c)=0f'(c) = 0 and f(c)<0f''(c) < 0, then ff has a relative maximum at x=cx = c because the graph is concave down at this critical point.

Correct Answer

Cff has a relative maximum at x=cx = c.

More Unit 5: Analytical Applications of Differentiation practice questions

Try a random question →

Practice more AP Calculus AB questions with full explanations

Practice Unit 5: Analytical Applications of Differentiation Questions →