AP®︎ Calculus AB: 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 AB – Using the First Derivative Test to Determine Relative (Local) Extrema.

Questions List

Topic 5.4

Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
Q12
Q13
Q14
Q15

Question 1 Easy

Let ff be differentiable for all real xx. Suppose f′(x)>0f'(x)>0 for x<−1x<-1, f′(−1)=0f'(-1)=0, and f′(x)<0f'(x)<0 for x>−1x>-1.

Which must be true about ff at x=−1x=-1?

Aff has a relative maximum at x=−1x=-1.
Bff has neither a relative maximum nor a relative minimum at x=−1x=-1.
Cf(−1)=0f(-1)=0.
Dff has a relative minimum at x=−1x=-1.

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 5.4: 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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