AP®︎ Calculus AB: Topic 5.2 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 5.2 of AP Calculus AB – Extreme Value Theorem, Global Versus Local Extrema, and Critical Points.

Questions List

Topic 5.2

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Question 1 Easy

Let ff be a function defined on the closed interval [a,b][a,b], and let cc be a number in [a,b][a,b]. Which of the following means that ff has a global maximum on [a,b][a,b] at x=cx=c?

Af′(c)=0f'(c)=0.
Bf(c)≤f(x)f(c)\leq f(x) for every xx in [a,b][a,b].
Cf(c)≥f(x)f(c)\geq f(x) for every xx in [a,b][a,b].
DThere is an open interval containing cc such that f(c)≥f(x)f(c)\geq f(x) for every xx in both that interval and [a,b][a,b].

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 5.2: Extreme Value Theorem, Global Versus Local Extrema, and Critical Points

Learning Objective: FUN-1.C

Justify conclusions about functions by applying the Extreme Value Theorem.

Essential Knowledge: FUN-1.C.1

If a function f is continuous over the interval (a, b), then the Extreme Value Theorem guarantees that f has at least one minimum value and at least one maximum value on [a, b].

Essential Knowledge: FUN-1.C.2

A point on a function where the first derivative equals zero or fails to exist is a critical point of the function.

Essential Knowledge: FUN-1.C.3

All local (relative) extrema occur at critical points of a function, though not all critical points are local extrema.

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