Let $~a\lt b\lt c\lt d$，proof that if $f$ is a convex function both in $[a,c]$ and $[b,d]$, $f$ is convex in $[a,d]$
How to prove the real value function $f$ is convex on $[a,d]$ if $f$ is convex on both $[a,c]$ and $[b,d]$? ($a<b<c<d$).