Let $f(x) = a_0 + a_1|x| + a_2|x|^2 + a_3|x|^3$, where $a_0, a_1, a_2, a_3$ are constants. Then $f'(x)$ exists at $x = 0$ if and only if (A) $a_1 = 0$ (B) $a_1 = 0$ and $a_2 = 0$ (C) $a_1 = 0$ and $a_3 = 0$ (D) $a_2 = 0$ and $a_3 = 0$
Let $f(x) = a_0 + a_1|x| + a_2|x|^2 + a_3|x|^3$, where $a_0, a_1, a_2, a_3$ are constants. Then $f'(x)$ exists at $x = 0$ if and only if\\
(A) $a_1 = 0$\\
(B) $a_1 = 0$ and $a_2 = 0$\\
(C) $a_1 = 0$ and $a_3 = 0$\\
(D) $a_2 = 0$ and $a_3 = 0$