Theorems · Theorem · real analysis

ConcaveOn.antitoneOn_slope_gt

∀ {𝕜 : Type u_1} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] {s : Set 𝕜} {f : 𝕜 → 𝕜} {x : 𝕜},
  ConcaveOn 𝕜 s f → x ∈ s → AntitoneOn (slope f x) {y | y ∈ s ∧ x < y}

Defined in

Mathlib.Analysis.Convex.Deriv

Cited by

0 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRing