#### 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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Solution 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.