Question

Let $f:R\to R$ be a function defined by $f\left(x\right)=max\{x,x^3\}$. The set of all points where $f\left(x\right)$ is NOT differentiable is:

• A. $\{-1,1\}$
• B. $\{-1,0\}$
• C. $\{0,1\}$
• D. $\{-1,0,1\}$

Answer 1

Answer: (D)

$\{-1,0,1\}$

$f\left(x\right)=m\{x,x^3\}$

$=x;x<-1$ and

$=x^3;-1\le x\le 0$

$\Rightarrow f\left(x\right)=x;0\le x\le 1$ and

$=x^3;x\ge 1$

$\therefore f\left(x\right)=1;x<-1$

$\therefore f^{\prime }\left(x\right)=3x^2;-1\le x\le 0$ and $=1$

$0<x<1$

Hence, option D is correct.