AP®︎ Calculus BC: Topic 1.16 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 1.16 of AP Calculus BC – Working with the Intermediate Value Theorem (IVT).

Questions List

Topic 1.16

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Question 1 Easy

The Intermediate Value Theorem concludes that there is a number cc with a<c<ba<c<b such that f(c)=df(c)=d. Which of the following are the hypotheses that guarantee this conclusion?

Aff is increasing on [a,b][a,b], and dd is strictly between f(a)f(a) and f(b)f(b).
Bff is continuous on [a,b][a,b], and f(a)<f(b)f(a)<f(b).
Cff is continuous on [a,b][a,b], and f(a)f(a) and f(b)f(b) have opposite signs.
Dff is continuous on [a,b][a,b], and dd is strictly between f(a)f(a) and f(b)f(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 1.16: Working with the Intermediate Value Theorem (IVT)

Learning Objective: FUN-1.A

Explain the behavior of a function on an interval using the Intermediate Value Theorem.

Essential Knowledge: FUN-1.A.1

If f is a continuous function on the closed interval [a, b] and d is a number between f(a) and f(b), then the Intermediate Value Theorem guarantees that there is at least one number c between a and b, such that f(c) = d.

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