Intermediate Value Theorem Worksheet
Explore the Intermediate Value Theorem with this worksheet, featuring questions on its application to continuous functions and finding roots.
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Intermediate Value Theorem
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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 Intermediate Value Theorem in your own words.
2. Which of the following is a necessary condition for the Intermediate Value Theorem to apply to a function f(x) on an interval [a, b]?
f(x) must be differentiable on (a, b).
f(x) must be continuous on [a, b].
f(a) and f(b) must have the same sign.
f(x) must be linear on [a, b].
3. If f(x) is a continuous function on the interval [1, 5] and f(1) = 2 and f(5) = 10, then by the Intermediate Value Theorem, there must exist a value c in the interval (1, 5) such that f(c) = .
4. Use the Intermediate Value Theorem to show that the function f(x) = x³ - 4x + 1 has a root in the interval [0, 1].
5. The Intermediate Value Theorem guarantees that a function f(x) will take on every value between f(a) and f(b) on the interval [a, b] even if f(x) is not continuous on [a, b].
True
False