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Mean Value Theorem Worksheet

A Grade 11 Calculus worksheet covering the Mean Value Theorem with various question types.

Grade 11 Math CalculusMean Value Theorem
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Includes

True / FalseFill in the BlanksMultiple Choice2 Short Answer

Standards

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

Topics

CalculusMean Value TheoremDerivativesContinuityDifferentiability
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 work for full credit.

1. The Mean Value Theorem applies to any continuous function on a closed interval.

T

True

F

False

2. If a function is differentiable on an open interval (a,b), then it is also continuous on [a,b].

T

True

F

False

3. The Mean Value Theorem states that if a function f is   on the closed interval [a,b] and   on the open interval (a,b), then there exists a number c in (a,b) such that f'(c) =  .

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

a

f(x) = |x|

b

f(x) = 1/x

c

f(x) = x^2

d

f(x) = tan(x)

5. Verify that the function f(x) = x^3 - 3x^2 + x on the interval [0, 3] satisfies the conditions of the Mean Value Theorem. Then, find all values of c that satisfy the conclusion of the theorem.

6. A car travels a distance of 180 miles in 3 hours. Use the Mean Value Theorem to explain why at some point during the trip, the car's instantaneous speed must have been exactly 60 mph.