Answer by Reveillark for Continuously differentiable function of a convex set
There's a slight issue with your use of quantifiers. Let's look closer at what's going on.Fix $x,y\in V$. Define a new function $g:[0,1]\to\mathbb{R}$ by $g(t)=f(ty+(1-t)x)$. This is well defined...
View ArticleContinuously differentiable function of a convex set
I have an analysis problem that I am trying to work through.The problem:Let $V$ be a convex open set in $R^2$ and let $f: V\to R$ be continuously differentiable in V. Show that if there is a positive...
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