#### Question

State Rolle's theorem ?

#### 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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Solution for question: State Rolle'S Theorem ? concept: Maximum and Minimum Values of a Function in a Closed Interval. For the courses CBSE (Science), CBSE (Commerce), CBSE (Arts), PUC Karnataka Science