Question

The set of all points where $f\left(x\right)=\sqrt[3]{3x^2\left|x\right|}-\left|x\right|-1$ is not differentiable is

• A. $\left\{0\right\}$
• B. $\{-1,0,1\}$
• C. $\{0,1\}$
• D. None of these

Answer 1

Answer: (D)

None of these

When $x>0$ the the function is $\sqrt[3]{3x^3}-x-1$ which is = $-1$

Now when $x<0$ then the function is $\sqrt[3]{3{-x}^3}+x-1=-1$

Now when $x=0$ then also the function is $-1$ so the function is differentiable at all points. Slope is equal to zero