If
$$f(x) = \begin{cases}-x-\frac{\pi}{2}, & x \leq -\frac{\pi}{2}\\-\cos x, & -\frac{\pi}{2}<x \leq 0\\x-1, & 0 < x \leq 1\\\ln x, & x > 1\end{cases}$$, then

A

f(x) is continuous at $$x = -\frac{\pi}{2}$$

B

f(x) is not differentiable at x =0

C

f(x) is differentiable at x=1

D

f(x) is differentiable at $$x = -\frac{3}{2}$$