Mean Value Theorem Worksheet
A Grade 11 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 work for full credit.
1. The Mean Value Theorem applies to any continuous function on a closed interval.
True
False
2. If a function is differentiable on an open interval (a,b), then it is also continuous on [a,b].
True
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]?
f(x) = |x|
f(x) = 1/x
f(x) = x^2
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.
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