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# Solution for Discuss the Applicability of Lagrange'S Mean Value Theorem for the Function F(X) = | X | on [−1, 1] ? - CBSE (Commerce) Class 12 - Mathematics

ConceptMaximum and Minimum Values of a Function in a Closed Interval

#### Question

Discuss the applicability of Lagrange's mean value theorem for the function
f(x) = | x | on [−1, 1] ?

#### Solution

Given:

$f\left( x \right) = \left| x \right|$

If Lagrange's theorem is applicable for the given function, then $f\left( x \right)$ is continuous on $\left[ - 1, 1 \right]$ and differentiable on $\left( - 1, 1 \right)$ But it is known that $f\left( x \right) = \left| x \right|$ is not differentiable at $x = 0 \in \left( - 1, 1 \right)$ .

Thus, our supposition is wrong.
Therefore, Lagrange's theorem is not applicable for the given function.

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#### APPEARS IN

Solution for question: Discuss the Applicability of Lagrange'S Mean Value Theorem for the Function F(X) = | X | on [−1, 1] ? concept: Maximum and Minimum Values of a Function in a Closed Interval. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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