Question

Show that the lagrange's mean value theorem is not applicable to the function
f(x) = $\frac{1}{x}$ on [−1, 1]

Answer 1

Given:
$f\left(x\right)=\frac{1}{x}$

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 $\left[-1,1\right]$.1x