AP®︎ Calculus BC: Topic 5.7 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 5.7 of AP Calculus BC – Using the Second Derivative Test to Determine Extrema.

Questions List

Topic 5.7

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Q9

Question 1 Easy

The function ff is twice differentiable for all xx, with f′(3)=0f'(3)=0 and f′′(3)=−2f''(3)=-2. Which of the following is true?

Aff has a relative minimum at x=3x=3.
BThe graph of ff has a point of inflection at x=3x=3.
Cff has a relative maximum at x=3x=3.
DWhether ff has a relative extremum at x=3x=3 cannot be determined.

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Calculus BC Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.

Topic 5.7: Using the Second Derivative Test to Determine Extrema

Learning Objective: FUN-4.A

Justify conclusions about the behavior of a function based on the behavior of its derivatives.

Essential Knowledge: FUN-4.A.7

The second derivative of a function may determine whether a critical point is the location of a relative (local) maximum or minimum.

Essential Knowledge: FUN-4.A.8

When a continuous function has only one critical point on an interval on its domain and the critical point corresponds to a relative (local) extremum of the function on the interval, then that critical point also corresponds to the absolute (global) extremum of the function on the interval.

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