The problem:
Let f(x) = x[sup:22jqxo3c]2[/sup:22jqxo3c] (x < 0), f(x) = x[sup:22jqxo3c]3[/sup:22jqxo3c] (x >= 0).
(a) Find f'(0).
(b) Does f''(0) exist?
My work so far:
(a) f'(x) = 2x (x < 0), f'(x) = 3x[sup:22jqxo3c]2[/sup:22jqxo3c] (x ? 0) ? f'(0) = 3(0)[sup:22jqxo3c]2[/sup:22jqxo3c] = 0
(b) f''(x) = 2 (x < 0), f''(x) = 6x (x ? 0) ? f''(0) = 6(0) = 0
My textbook gives 0 as the answer to part (a), but "no" to the answer of part (b). Why does f''(0) not exist, and did I arrive at the answer to part (a) correctly?
Let f(x) = x[sup:22jqxo3c]2[/sup:22jqxo3c] (x < 0), f(x) = x[sup:22jqxo3c]3[/sup:22jqxo3c] (x >= 0).
(a) Find f'(0).
(b) Does f''(0) exist?
My work so far:
(a) f'(x) = 2x (x < 0), f'(x) = 3x[sup:22jqxo3c]2[/sup:22jqxo3c] (x ? 0) ? f'(0) = 3(0)[sup:22jqxo3c]2[/sup:22jqxo3c] = 0
(b) f''(x) = 2 (x < 0), f''(x) = 6x (x ? 0) ? f''(0) = 6(0) = 0
My textbook gives 0 as the answer to part (a), but "no" to the answer of part (b). Why does f''(0) not exist, and did I arrive at the answer to part (a) correctly?
