ConcaveOn.antitoneOn_deriv

∀ {S : Set ℝ} {f : ℝ → ℝ}, ConcaveOn ℝ S f → (∀ x ∈ S, DifferentiableAt ℝ f x) → AntitoneOn (deriv f) S

If f is concave on S and differentiable at all points of S, then its derivative is antitone (monotone decreasing) on S.

Defined in: Mathlib.Analysis.Convex.Deriv
Cited by: 0 results in Mathlib
Foundations: Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

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