Here's a homework question I'm struggling with:
Let $f,g$ two convex functions. Prove that $h(x)=\max\{f(x),g(x)\}$ is also convex
I don't know where to begin. The only thing I had in mind was was to try proving that if a function is convex on two sets $A$ and $B$, it is also convex on their union. That does not seem right though, for example if I glue together $f(x)=x^2, g(x)=\frac{x^2}{1000}$ where $f$ is defined on $[0,1]$ and $g$ on $(1,2]$.
Anyway, that was the only thing I thought about. Any better ideas? thanks!
\max
instead ofmax
(similarly use\sin
instead ofsin
etc) $\endgroup$ – user17762 May 20 '12 at 17:54