Question

In $[0,1]$ Lagranges Mean Value theorem is NOT applicable to

• A. $f(x)=\{\begin{array}{ll}\frac{1}{2}-x& x<\frac{1}{2}\\ {\left(\frac{1}{2}-x\right)}^2& x\ge \frac{1}{2}\end{array}$
• B. $f(x)=\{\begin{array}{ll}\frac{\sin x}{x},& x\ne 0\\ 1,& x=0\end{array}$
• C. $f(x)=x|x|$
• D. $f(x)=|x|$

Answer 1

Answer: (A)

The function defined in $(a)$ is not differentiable at $x=1/2$.