#### Question

Show that the lagrange's mean value theorem is not applicable to the function

f(x) = \[\frac{1}{x}\] on [−1, 1] ?

#### Solution

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 \[\left[ - 1, 1 \right]\]

Is there an error in this question or solution?

Solution Show that the Lagrange'S Mean Value Theorem is Not Applicable to the Function F(X) = 1 X on [−1, 1] ? Concept: Maximum and Minimum Values of a Function in a Closed Interval.