Let $$f:R \rightarrow R$$ be given by
$$f(x) = \begin{cases}x^5 + 5x^4 + 10x^3 + 10x^2 + 3x +1 & x < 0;\\x^2 - x + 1, & 0 \leq x \leq 1; \\\frac{2}{3}x^3 - 4x^2 + 7x - \frac{8}{3}, & 1 \leq x < 3;\\ (x - 2) \log_e(x - 2) - x + \frac{10}{3}, & x \geq 3. \end{cases}$$
Then which of the following options is/are correct?

A

f is increasing on $$(-\infty, 0)$$

B

f' has a local maximum at x = 1

C

f is onto

D

f' is NOT differentiable at x = 1