Theorems · Theorem · real analysis
StrictConcaveOn.derivWithin_lt_slope
∀ {S : Set ℝ} {f : ℝ → ℝ} {x y : ℝ},
StrictConcaveOn ℝ S f → x ∈ S → y ∈ S → x < y → DifferentiableWithinAt ℝ f S y → derivWithin f S y < slope f x y- Defined in
- Mathlib.Analysis.Convex.Deriv
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- DifferentiableWithinAtstatement and proof · cited by 453
- derivWithinstatement · cited by 258
- slopestatement · cited by 147
- DifferentiableWithinAt.hasDerivWithinAtproof · cited by 85
- StrictConcaveOnstatement and proof · cited by 85
- StrictConcaveOn.lt_slope_of_hasDerivWithinAtproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- StrictConcaveOn.strictAntiOn_derivWithinproof · cited by 0