Let $f:\Bbb R \to \Bbb R$ be a $C^1$ function, and let $E \subset \Bbb R$ be a jordan measurable set. Prove: $\; \partial f(E) \subseteq f(\partial E) $
Trying to prove it as part of another proof, been stuck for a while. Ideas?
2026-03-27 12:01:06.1774612866
Prove that $ \partial f(E) \subseteq f(\partial E) $
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This is not true. Say $E=[-1,1]$ and $f(x)=x^2$. Then $\partial f(E)=\{0,1\}$ and $f(\partial E)=\{1\}$.