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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

25 votes
2 answers
2k views

$f^3,f^2$ are the cube and quadratic of f respectively and both infinite differentiable on $...

Let $f$ be a real function with domain R. If $f^2$ and $f^3$ are both infinitely differentiable on R, how to prove $f$ is infinitely differentiable on R? I have been thinking about this problem for a …
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