AP®︎ Calculus AB: 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 AB – Using the Second Derivative Test to Determine Extrema.

Questions List

Topic 5.7

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Question 1 Easy

Let ff be a twice-differentiable function with f′(3)=0f'(3)=0 and f′′(3)=−5f''(3)=-5.

Which of the following is true at x=3x=3?

Aff has a relative maximum at x=3x=3.
Bff has a point of inflection at x=3x=3.
Cff has neither a relative maximum nor a relative minimum at x=3x=3.
Dff has a relative minimum at x=3x=3.

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Calculus AB 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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