Mean Value Theorem Worksheet
A Grade 12 Calculus worksheet covering the Mean Value Theorem with various question types.
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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. Which of the following conditions is NOT required for the Mean Value Theorem to apply to a function f(x) on a closed interval [a, b]?
f(x) is continuous on [a, b]
f(x) is differentiable on (a, b)
f(a) = f(b)
f'(x) exists on (a, b)
2. For the function f(x) = x^2 on the interval [0, 2], what is the value of c guaranteed by the Mean Value Theorem?
0
1
2
Does not exist
1. 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 at least one number c in (a, b) such that f'(c) = .
2. Rolle's Theorem is a special case of the Mean Value Theorem where f(a) = .
1. Verify the Mean Value Theorem for the function f(x) = x^3 - 3x on the interval [0, 2]. Find all values of c that satisfy the theorem.
1. If a function is differentiable on (a, b), it must also be continuous on [a, b].
True
False
2. The Mean Value Theorem can be applied to f(x) = |x| on [-1, 1].
True
False
The graph below shows a function f(x) on the interval [a, b].
1. Does the Mean Value Theorem apply to the function shown on the interval [a, b]? Explain why or why not.