Mathematics Differential Calculus Differentiability

Let f(x) = a0 + a1|x| + a2|x|2 + a3|x|3, where a0, a1, a2, a3 are real constants. Then f(x) is differentiable at x = 0

1
whatever be a0, a1, a2, a3
2
for no values of a0, a1, a2, a3
3
only if a1 = 0
4
only if a1 = 0, a3 = 0

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