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Rolle’s Theorem
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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
![Rolle’s Theorem Let f be a function that satisfies the following three hypotheses: 1) f is continuous on [ a, b]](http://slideplayer.com/slide/14578252/90/images/2/Rolle%E2%80%99s+Theorem+Let+f+be+a+function+that+satisfies+the+following+three+hypotheses%3A+1%29+f+is+continuous+on+%5B+a%2C+b%5D.jpg "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.")
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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.
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Example Use Rolle’s Theorem to find all values of c such that f’(c) = 0 between the intercepts of the function
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