Theorems · Theorem · real analysis
StrictConcaveOn.slope_lt_of_hasDerivAt
∀ {S : Set ℝ} {f : ℝ → ℝ} {x y f' : ℝ},
StrictConcaveOn ℝ S f → x ∈ S → y ∈ S → x < y → HasDerivAt f f' x → slope f x y < f'- Defined in
- Mathlib.Analysis.Convex.Deriv
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- neg_negproof · cited by 960
- HasDerivAtstatement and proof · cited by 493
- slopestatement and proof · cited by 147
- StrictConcaveOnstatement and proof · cited by 85
- neg_lt_negproof · cited by 20
- HasDerivAt.negproof · cited by 14
- StrictConcaveOn.negproof · cited by 11
- slope_negproof · cited by 10
- StrictConvexOn.lt_slope_of_hasDerivAtproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- StrictConcaveOn.slope_lt_derivproof · cited by 0