Theorems · Theorem · real analysis
StrictConcaveOn.slope_lt_deriv
∀ {S : Set ℝ} {f : ℝ → ℝ} {x y : ℝ},
StrictConcaveOn ℝ S f → x ∈ S → y ∈ S → x < y → DifferentiableAt ℝ f x → slope f x y < deriv f x- Defined in
- Mathlib.Analysis.Convex.Deriv
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- derivstatement · cited by 676
- DifferentiableAtstatement and proof · cited by 617
- slopestatement · cited by 147
- DifferentiableAt.hasDerivAtproof · cited by 114
- StrictConcaveOnstatement and proof · cited by 85
- StrictConcaveOn.slope_lt_of_hasDerivAtproof · cited by 1
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