Let the function $$f$$ be given by

$$f(x) = \begin{cases}-(x -1)^4; & x \leq 2\\(x - 3)^3; & x > 2\end{cases}$$

Then local extrema of $$f$$ exist at

A

$$x = 1$$ and $$x = 3$$

B

$$x = 1$$ and $$x = 2$$

C

$$x = 2$$ and $$x = 3$$

D

$$x = 1, x = 2$$ and $$x = 3$$