Question

The total number of points of non-differentiability of
$f\left(x\right)=max\{{\sin }^{2}x,{\cos }^{2}x,\frac{3}{4}\}$ in $[0,10\pi ]$, is

Answer 1

Since, ${\sin }^{2}x$ and ${\cos }^{2}x$ are periodic with period $\pi$ and in $[0,\pi ]$, there are four points of non-differentiability of $f\left(x\right)$ if we follow the path along $max\{{\sin }^{2}x,{\cos }^{2}x,\frac{3}{4}\}$ as it is evident from the graph below.
$\therefore$ In $[0,10\pi ],$ there are $40$ points of non- differentiability.