AP®︎ Calculus BC: Topic 5.4 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 5.4 of AP Calculus BC – Using the First Derivative Test to Determine Relative (Local) Extrema.

Questions List

Topic 5.4

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Q2
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Q7
Q8
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Q10
Q11
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Q14
Q15

Question 1 Easy

Let ff be differentiable for all real xx, with f′(3)=0f'(3)=0. Suppose f′(x)>0f'(x)>0 for 2<x<32<x<3 and f′(x)<0f'(x)<0 for 3<x<43<x<4.

Which statement about ff at x=3x=3 is true?

Aff has a relative minimum at x=3x=3.
Bff has neither a relative maximum nor a relative minimum 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 without a formula for ff.

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 5.4: Using the First Derivative Test to Determine Relative (Local) 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.2

The first derivative of a function can determine the location of relative (local) extrema of the function.

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