(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose a function f is continuous and has continuous derivatives of all orders for all

x. it satisfies xf ''(x) + f '(x) + xf(x) = 0. Given f(0) = 1

find the value of f '(0) and f '' (0).

2. Relevant equations

3. The attempt at a solution

when x=0,

0f''(0) + f ' (0) + 0f(0) = 0

therefore f ' (0) = 0

Now, I am not sure on how to find f ''(0). Is it undefined?

Thanks for your help.

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# Homework Help: Differentiation question with continuity

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