Let $r>0$ and $f: K_r(0)\to \mathbb R$ with
$$\exists C>0\;\forall x\in K_r(0): |f(x)|\le Cx^2 $$
Show that $f$ is differentiable at $x=0$.
Show that a function bounded by $Cx^2$ is differentiable at $x=0$.
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$\begingroup$
derivatives
inequality
limits-without-lhopital
1 Answers
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By the given property $|f(0)|\le C0^2=0$ which implies that $f(0)=0$. Hence, for $h
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0yeah I tried the same exactly and i wanted to show it using Espilon_Proof but somehow i can t figure that out – 2017-01-04
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0The $\epsilon$ proof is essentially the same. – 2017-01-04
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0i think i know what should i do , i will use sandwich Theorem :D thnx – 2017-01-04