Let $U$ be a connected open subset of $ \Bbb R^n$ and $f: U \to \Bbb R^m$ is twice-differentiable everywhere and $(D^2f)_p=0$ for all $p$. How do I show that $f$ is linear?
2026-05-04 18:12:18.1777918338
Proving linearity of a twice-differentiable function with $(D^2 f)_p =0$
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