∀ {D : Set ℝ},
  Convex ℝ D →
    ∀ {f : ℝ → ℝ},
      ContinuousOn f D →
        DifferentiableOn ℝ f (interior D) →
          DifferentiableOn ℝ (deriv f) (interior D) → (∀ x ∈ interior D, 0 ≤ deriv^[2] f x) → ConvexOn ℝ D f