Mean Value Theorem Worksheet

Explore the Mean Value Theorem with these practice problems for Grade 9 Calculus students.

Grade 9 Math CalculusMean Value Theorem

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2 Short AnswerMultiple ChoiceFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HS.C.A.3

Topics

CalculusMean Value TheoremDerivativesGrade 9 Math

7 sections · Free to use · Printable

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Mean Value Theorem Worksheet

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Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. State the conditions that a function must satisfy for the Mean Value Theorem to apply on a closed interval [a, b].

2. Which of the following functions satisfies the conditions of the Mean Value Theorem on the interval [-1, 1]?

f(x) = |x|

f(x) = 1/x

f(x) = x^2

f(x) = tan(x)

3. For the function f(x) = x^3 - 3x on the interval [0, 2], the value of c that satisfies the Mean Value Theorem is approximately .

4. Given the function f(x) = e^x on the interval [0, 1], find the value of c that satisfies the conclusion of the Mean Value Theorem. Show your work.

5. If a function is continuous on [a, b] and differentiable on (a, b), then there is at least one point c in (a, b) such that f'(c) equals the average rate of change of f on [a, b].

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False