Rolle's Theorem, "Let f be a continuous function on [a,b] that is differentiable on (a,b) and...

Rolle's Theorem, "Let f be a continuous function on [a,b] that is differentiable on (a,b) and such that f(a)=f(b). Then there exists at least one point c on (a,b) such that f'(c)=0."

Rolle's Theorem requires three conditions be satisified.

(a) What are these three conditions?

(b) Find three functions that satisfy exactly two of these three conditions, but for which the conclusion of Rolle's theorem does not follow, i.e., there is no point c in (a,b) such that f'(c)=0. Each function should satisfy a different pair of conditions than the other two functions. For each function you should give a definition, a graph, and a short justification of its failing to meet the conclusion of Rolle's Theorem.

Expert Solution

Colby Messinger answered 1 year ago

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Rolle's Theorem, "Let f be a continuous function on [a,b] that is differentiable on (a,b) and...

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