Question

LMVT is applicable for

• A. $f\left(x\right)=|x|$ in $[-1,2]$
• B. $f\left(x\right)=\ln x$ in $[1,e]$
• C. $f\left(x\right)=x-\frac{1}{x}$ in $[1,3]$
• D. $f\left(x\right)=\sqrt{x^2-4}$ in $[2,4]$

Answer 1

Answer: (B), (C), (D)

$f\left(x\right)=\sqrt{x^2-4}$ in $[2,4]$

$|x|$ is not differentiable at $x=0$. So, LMVT can't be applied.
All the remaining options satisfy the LMVT conditions.