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# Rolles Theorem for AP Calculus

based on 4 ratings
By McGraw-Hill Professional
Updated on Oct 24, 2011

Practice problems for these concepts can be found at:  Graphs of Functions and Derivatives Practice Problems for AP Calculus

If f is a function that satisfies the following three conditions:

1. f is continuous on a closed interval [a, b]
2. f is differentiable on the open interval (a, b)
3. f(a) = f(b) = 0

then there exists a number c in (a, b) such that f '(c) = 0. (See Figure 7.1-1.)

Note that if you change condition 3 from f(a)= f(b)=0 to f(a)= f(b), the conclusion of Rolle's Theorem is still valid.

Practice problems for these concepts can be found at:  Graphs of Functions and Derivatives Practice Problems for AP Calculus

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