Show that the lagranges mean value theorem is not applicable to the function `f(x)=1/x` on `[-1,\ 1]` .

Answer

LMVT is not applicable for the function `f(x)=1 / x` on `[-1,1]`

Explanation

ATQ, `f(x)=(1 / x)` on `[-1,1]`

As we know, `x \ne 0`


`\Rightarrow f(x)` exists for all the values of `x` except 0

`\Rightarrow f(x)` is the discontinuous at `x=0`


So, `f(x)` is not continuous in `[-1,1]`

Thus, LMVT is not applicable for the function `f(x)=1 / x` on `[-1,1]`