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 October 29th, 2011, 05:46 PM #1 Newbie   Joined: Oct 2011 Posts: 14 Thanks: 0 differentiable function Find all p and q $p,q>0$that function $f: \mathbb{R}^n \rightarrow \mathbb{R}$ $f(x)=\left( \sum^n_{i=1} |x_1|^p \right) ^{\frac{1}{q}}$ is defferentiable in $0 \in \mathbb{R}^n$. Does anyone give any clue?
 October 31st, 2011, 02:09 PM #2 Member   Joined: Nov 2009 From: France Posts: 98 Thanks: 0 Re: differentiable function We can show that $f$ is differentiable if $p>q$ (I guess it's $x_i$ in the sum) (the identically  map is the differential), and not differentiable if $p. In the case $p=q$, consider the two sub-cases $p>1$ or $p\leq 1$.

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