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Question
Show that the lagrange's mean value theorem is not applicable to the function
f(x) = \[\frac{1}{x}\] on [−1, 1] ?
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Solution
Given:
Clearly, \[f\left( x \right)\] does not exist for x = 0
Thus, the given function is discontinuous on \[\left[ - 1, 1 \right]\] .
Hence, Lagrange's mean value theorem is not applicable for the given function on \[\left[ - 1, 1 \right]\]
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