# Functionally impossible.

Calculus Level 5

$$f(x)$$ is defined for $$x\ge0$$ and has a continuous derivative. It satisfies $$f(0)=1, f^{'}(0)=0$$ and $$[1+f(x)]f^{''}(x)=1+x$$. Let $$f(1)= A$$, then the impossible values of $$A$$ is/are:

Comment:

I worked really hard to get $$Lv.5$$ in calculus, just so that I could post this question. Please also give solution. Much thanks.

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