EDB — 18K

Exercises

1. [18K]Prove that a continuous function \(f : (a, b) → ℝ\) is convex if and only if, for every \(u, v ∈ (a, b)\),

   \[ f\left(\frac{u+v} 2\right) ≤ \frac{f (u) + f (v)} 2\quad . \]