Differentiability Questions in English

(B) For $x \neq 0$,$f(x) = |\frac{\sin x}{x}|$.
Critical points occur where $f'(x) = 0$ or $f'(x)$ is undefined.
$1$. At $x = 0$,$f(x)$ is continuous and has a local maximum,so $x = 0$ is a critical point.
$2$. For $x \neq 0$,$f(x) = 0$ when $\sin x = 0$,which gives $x = \pm \pi$ in the interval $(-2\pi, 2\pi)$. At these points,the function is not differentiable because of the absolute value,so $x = \pm \pi$ are critical points.
$3$. We also check for $f'(x) = 0$ where $\frac{\sin x}{x} \neq 0$. This requires $\frac{x \cos x - \sin x}{x^2} = 0$,or $\tan x = x$. The roots of $\tan x = x$ (other than $x=0$) are approximately $\pm 4.49$,which lie outside the interval $(-2\pi, 2\pi)$ since $2\pi \approx 6.28$.
Thus,the critical points in $(-2\pi, 2\pi)$ are $x = 0, \pi, -\pi$.
Total number of critical points is $3$.