Question

Consider the function $f\left(x\right)=max\left\{\left|sin x\right| , \left|cos ⁡ x\right|\right\},\forall x\in \left[0,3 \pi \right]$ . If $\lambda $ is the number of points at which $f\left(x\right)$ is non-differentiable, then the value of $\lambda $ is

Answer 1

Using graph of $\left|sin x\right|\&\left|cos ⁡ x\right|$ , we get,
$f\left(x\right)$ is non differentiable at

$x_{1}=\frac{\pi }{4},x_{2}=\frac{3 \pi }{4},x_{3}=\frac{5 \pi }{4},$ $x_{4}=\frac{7 \pi }{4},x_{5}=\frac{9 \pi }{4},x_{6}=\frac{11 \pi }{4}$
Hence, $\lambda =6$