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Question: please help i am so lost...

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Q5. The goal of this question is to show that while an analytic function is necessarily infinitely continuously differentiable (we say that φ is CM) but a Coo function is not necessarily analytic. We do this by a counterexample, i.e, by funding an example of a C°° function which is not analytic near a point Co, i.e, it cannot be written as a power series near xo. Consider the function 0 if 0 (a) Show that φ(x) is Coo and that φ(n)(0) = 0, n = 0, 1, 2, Note that in order to show that ф and all its derivatives, Ф(n), are continuous and differentiable at x - 0, you need to use the formal definitions of continuity and differentiability, namely, that φ(n) (0) = lim φ(n) (X) and that φ(n+1) (0) = lim exists and is finite. (b) Deduce that φ(x) is not analytic.Please help! I am so lost!!!

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