Let $$f(x) =\begin{cases}x+1&x<0\\(x-1)^2&x≥0.\end{cases}$$Which one of the following is true?
(a) f is differentiable on R
(b) f has neither a local maximum nor a local minimum in R
(c) f is bounded on R
(d) f is not differentiable at x =0 and f(x) has local maximum at x = 0.
I know how f(x) is not differentiable at x = 0 but I'm not getting local maximum at x = 0.When I differentiate f(x) at x<0,f'(x)= 1,but when I differentiate when x>0,f'(x) = 2(x-1).
2(x-1)=0so, x = 1f''(x)= 2so, x=1 is a local minimum.