If f(x)= _ n=0 ^ n a_n|x|^n, where a_i's are real constants, then f(x) is

JEE Advanced Mathematics question

If , where 's are real constants, then is

(A)continuous at for all Correct
(B)differentiable at for all
(C)differentiable at for all Correct
(D)none of these

Answer: (A),(C)

Solution

(The sum means .)

- (a) ✓: each is continuous, and a finite linear combination of continuous functions is continuous. - Differentiability at : for , , so **every** with is

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Question ID VK-109344