Theorems · Theorem · real analysis
StrictConvexOn.rightDeriv_lt_slope
∀ {S : Set ℝ} {f : ℝ → ℝ} {x y : ℝ},
StrictConvexOn ℝ S f →
x ∈ S → y ∈ S → x < y → DifferentiableWithinAt ℝ f (Set.Ioi x) x → derivWithin f (Set.Ioi x) x < slope f x y- Defined in
- Mathlib.Analysis.Convex.Deriv
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Set.Ioistatement and proof · cited by 1,463
- DifferentiableWithinAtstatement and proof · cited by 453
- derivWithinstatement · cited by 258
- slopestatement · cited by 147
- DifferentiableWithinAt.hasDerivWithinAtproof · cited by 85
- StrictConvexOnstatement and proof · cited by 84
- StrictConvexOn.lt_slope_of_hasDerivWithinAt_Ioiproof · cited by 4
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