Discuss the applicability of Lagranges mean value theorem for the function `f(x)=|x|` on `[-1,\ 1]` .

Answer

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

Explanation

Given as `f(x)=|x|` on `[-1,1]`


$$ Therefore, f(x) \text { can be defined as } =\left\{\begin{array}{lc}-x, & x<0 \\ x, & x \geq 0\end{array}\right.` $$
For the differentiability at `x=0`,
$$
\begin{aligned}
&L H D=\lim _{x \rightarrow 0^{-}} \frac{f(0-h)-f(0)}{-h} \\
...