#### Question

State Lagrange's mean value theorem ?

#### Solution

Lagrange's Mean Value Theorem:

Let \[f\left( x \right)\] be a function defined on \[\left[ a, b \right]\] such that

(i) it is continuous on \[\left[ a, b \right]\] and

(ii) it is differentiable on \[\left( a, b \right)\].

Then, there exists a real number \[c \in \left( a, b \right)\] such that

\[f'\left( c \right) = \frac{f\left( b \right) - f\left( a \right)}{b - a}\] .

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