A function has a relative maximum at x = c when:

A f'(c) > 0

B f'(c) = 0 and f''(c) < 0

C f'(c) = 0 and f''(c) > 0

D f(c) = 0

✓ Correct Answer: Option B

By the second derivative test: if f'(c) = 0 and f''(c) < 0, the function is concave down at c → local maximum.

💡 Why is B) the correct answer?

The correct answer to the question "A function has a relative maximum at x = c when:" is Option B: f'(c) = 0 and f''(c) < 0.

The other options — A) f'(c) > 0, C) f'(c) = 0 and f''(c) > 0, D) f(c) = 0 — are incorrect for this AP Exam Prep question. As explained above: By the second derivative test: if f'(c) = 0 and f''(c) < 0, the function is concave down at c → local maximum.

📚 About This AP Exam Prep Practice Question

This 3-level AP Exam Prep question from the AP Calculus topic is part of BrainForge Quiz's free exam preparation library. Each question includes the correct answer and a detailed explanation to help you understand the underlying concept, not just memorize the answer.

How to use this page: Read the question above, consider all four options (A through D), then check the highlighted correct answer and explanation. For active timed practice, start a free AP Exam Prep practice test or use flashcards for spaced repetition review.

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A function has a relative maximum at x = c when:

✓ Correct Answer: Option B

📚 About This AP Exam Prep Practice Question

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