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Question

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

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Solution

Given:
fx=x

If Lagrange's theorem is applicable for the given function, then fx is continuous on -1, 1 and differentiable on -1, 1.

But it is known that fx=x is not differentiable at x=0-1, 1.

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


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