Theorems · Theorem · real analysis
ConcaveOn.slope_le_of_hasDerivWithinAt
∀ {S : Set ℝ} {f : ℝ → ℝ} {x y f' : ℝ},
ConcaveOn ℝ S f → x ∈ S → y ∈ S → x < y → HasDerivWithinAt f f' S x → slope f x y ≤ f'- Defined in
- Mathlib.Analysis.Convex.Deriv
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- HasDerivWithinAtstatement and proof · cited by 333
- ConcaveOnstatement and proof · cited by 159
- slopestatement · cited by 147
- Convex.ordConnectedproof · cited by 19
- HasDerivWithinAt.mono_of_mem_nhdsWithinproof · cited by 12
- Set.OrdConnected.mem_nhdsGTproof · cited by 4
- ConcaveOn.slope_le_of_hasDerivWithinAt_Ioiproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- ConcaveOn.slope_le_derivWithinproof · cited by 1