AP®︎ Calculus BC: Topic 5.6 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 5.6 of AP Calculus BC – Determining Concavity of Functions over Their Domains.

Questions List

Topic 5.6

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Question 1 Easy

Let ff be twice differentiable on a<x<ba<x<b, with f′′(x)<0f''(x)<0 for all xx in this interval.

Which of the following must be true on a<x<ba<x<b?

Aff is decreasing on a<x<ba<x<b.
Bf′f' is decreasing on a<x<ba<x<b.
Cf′(x)<0f'(x)<0 for all xx in a<x<ba<x<b.
Df(x)<0f(x)<0 for all xx in a<x<ba<x<b.

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 5.6: Determining Concavity of Functions over Their Domains

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.4

The graph of a function is concave up (down) on an open interval if the function’s derivative is increasing (decreasing) on that interval.

Essential Knowledge: FUN-4.A.5

The second derivative of a function provides information about the function and its graph, including intervals of upward or downward concavity.

Essential Knowledge: FUN-4.A.6

The second derivative of a function may be used to locate points of inflection for the graph of the original function.

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