Question

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

• A. $f\left(x\right)=x|x|$
• B. $f\left(x\right)=|x|$
• C. $f\left(x\right)=x$
• D. none of these

Answer 1

Answer: (D)

none of these

For Lagrange's mean value theorem to be applicable to a function in the in interval $[a,b]$, the function must be continuous and differentiable in the $[a,b]$.

A) $f\left(x\right)=x|x|$

$=x^2$ ..$x>0$

This is a quadratic function and so is continuous and differentiable in $R$

B) $f\left(x\right)=|x|$

$=x$ ..$x>0$

C) $f\left(x\right)=x$

Both these functions are linear and so they are continuous and differentiable in $R$

So, Lagrange's mean value theorem is applicable to all the given functions.

So, The answer is option (D).