Question

In $\left(\right. 0 , \, 2 \pi \left.\right)$ , the total number of points where $f\left(x\right)=max.\left\{sin x , cos ⁡ x , 1 - cos ⁡ x \, \right\}$ is not differentiable, are equal to

• A. $3$
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (A)

The graph of $f\left(x\right)=max.\left\{sin x , cos ⁡ x , 1 - cos ⁡ x \, \right\}$ is

$\Rightarrow $ $f\left(x\right)$ is not differentiable at $x = \frac{\pi }{4} , \, \frac{\pi }{2} , \, \frac{5 \pi }{3}$ .
$\Rightarrow $ $f\left(x\right)$ is not differentiable at $3$ points