Rolle’s Theorem.

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Presentation transcript:

Rolle’s Theorem

Rolle’s Theorem Let f be a function that satisfies the following three hypotheses: 1) f is continuous on [ a, b] 2) f is differentiable on [ a, b] 3) f(a) = f(b) Then there is a number c in [ a, b] such that f’(c) = 0

Example Verify that satisfies all 3 hypotheses of Rolle’s theorem over the interval [ 0, 2] and find all values of c that satisfy this conclusion.

Example Use Rolle’s Theorem to find all values of c such that f’(c) = 0 between the intercepts of the function