[18F] Show that \(f(x)\) is convex if and only if the map \(R(x,y)=\frac{f(x)-f(y)}{x-y}\) is monotonically weakly increasing in \(x\). 1 Moreover, \(f\) is strictly convex if and only if \(R\) is strictly increasing.
[18G]↺↻
