Let f(x) is a function defined as:-
\(f(x) = \left\{\begin{matrix}x^5+5x^4+3x^3+2x^2+1&;x<0\\\ x^2-x+1&;0\le x<1\\\ \frac{2}{3}x^3-4x^2+7x-\frac{8}{3}&;1\le x<3\\\ (x-2) \log_e(x-2)+10&;x\ge3\end{matrix}\right.\;\)
Which of the following statement is/are correct?
1
f'(x) has a local maxima at x = 1
2
f'(x) is NOT differentiable at x = 1
3
f'(x) has a local minima at x = 2
4
f'(x) has a local maxima at x =2