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AP®︎ Calculus BC: Topic 5.1 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 5.1 of AP Calculus BC – Using the Mean Value Theorem.

Questions List

Topic 5.1

Q10

Q11

Q12

Q13

Question 1 Easy

The function $f$ is continuous on $[2,6]$ and differentiable on $(2,6)$ .

Which of the following does the Mean Value Theorem guarantee?

AThere is a number

c

with

2<c<6

such that

f(c)=\dfrac{f(6)-f(2)}{6-2}

BThere is a number

c

with

2<c<6

such that

f'(c)=\dfrac{f(6)-f(2)}{6-2}

CAt the number

c=4

, the midpoint of the interval,

f'(c)=\dfrac{f(6)-f(2)}{6-2}

DThere is a number

c

with

2<c<6

such that

f'(c)=0

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 5.1: Using the Mean Value Theorem

Learning Objective: FUN-1.B

Justify conclusions about functions by applying the Mean Value Theorem over an interval.

Essential Knowledge: FUN-1.B.1

If a function f is continuous over the interval [a, b] and differentiable over the interval (a, b), then the Mean Value Theorem guarantees a point within that open interval where the instantaneous rate of change equals the average rate of change over the interval.

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AP®︎ Calculus BC: Topic 5.1 Practice Test

Question 1 Easy

What You’re Being Tested On:

Learning Objective FUN-1.B: FUN-1.B.1