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Question
State Rolle's theorem ?
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Solution
Rolle's Theorem:
Let f be a real valued function defined on the closed interval \[\left[ a, b \right]\] such that
(i) it is continuous on the closed interval \[\left[ a, b \right]\] ,
(ii) it is differentiable on the open interval \[\left( a, b \right),\] , and
(iii) \[f\left( a \right) = f\left( b \right)\]
Then, there exists a real number \[c \in \left( a, b \right)\] such that \[f'\left( c \right) = 0\] .
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