State Rolle's theorem. - Vidyadip

Question

State Rolle's theorem.

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Answer

Rolle's theorem: Let f(x) be a real value function defined on the closed interval [a, b] such that

It is continuous on [a, b]
It is differentiable on (a, b)
f(a) = f(b)

Then, there exists a real number $\text{c}\in(\text{a},\text{b})$ such that f'(c) = 0.

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