If $f(x)\left\{\begin{matrix}-x^2,&x≤0\\2,&x>0\end{matrix}\right.$, then

f(x) is a periodic function f(x) is an odd function f(x) is continuous at x = 0 f(x) is continuous at x = 1

f(x) is continuous at x = 0

f(x) is not continuous at x = 0, so not differentiable at x = 0.