Number of values of $x\in [0,\pi]$ where $f(x)=\lfloor 4\sin x-7\rfloor$ is non derivable is?
$f(x)=\lfloor 4\sin x-7\rfloor=\lfloor 4\sin x\rfloor-7$
I drew the graph of the $f(x)$ and see that there are six points in $x\in [0,\pi]$ where $f(x)$ is non-continuous and hence non derivable,but the answer given is $7$.
Let's work witn $g(x)=\lfloor 4\sin x\rfloor$ which jumps at the same points as $f$ does. There is a jump from 0 to 1, another from 1 to 2, another from 2 to 3, then it starts going down, one step down from 3 to 2, then one from 2 to 1, then from 1 to 0. So this would support the idea of only 6 jumps. But a graphing calculator would fail to notice the isolated jump at $x=\pi/2$ where the sine is $1$ for an isolated instant so that $g=4$ there, making yet another jump for a total of $7.$