Question

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

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

Answer 1

The correct option is D $\left\{\varphi \right\}$

$f\left(x\right)=\sqrt[3]{3x^2|x|}-\frac{\sqrt{1-{\cos }^{2}2x}|x|{\sec }^{2}x}{2\tan x}-1$
$f\left(x\right)=\sqrt[3]{3|x{|}^3}-|x|-1$
$f\left(x\right)=|x|-|x|-1$
$f\left(x\right)=-1$
Differentiable for all $x$