Concept explainers
Generalizing the Mean Value Theorem for
- a. Use Rolle’s Theorem to show that there is a number c in (a, b) such that
which is a generalization of the Mean Value Theorem for Integrals.
- b. Show that there is a number c in (a, b) such that
- c. Use a sketch to interpret part (b) geometrically.
- d. Use the result of part (a) to give an alternative proof of the Mean Value Theorem for Integrals.
(Source: The College Mathematics Journal, 33, 5, Nov 2002)
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