Theorems · Theorem · real analysis
ConvexOn.isMinOn_of_rightDeriv_eq_zero
∀ {S : Set ℝ} {f : ℝ → ℝ} {x : ℝ}, ConvexOn ℝ S f → x ∈ interior S → derivWithin f (Set.Ioi x) x = 0 → IsMinOn f S x- 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.
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
- Set.Ioistatement and proof · cited by 1,463
- interiorstatement and proof · cited by 714
- Eq.leproof · cited by 605
- LE.le.trans_eqproof · cited by 328
- derivWithinstatement and proof · cited by 258
- ConvexOnstatement and proof · cited by 232
- IsMinOnstatement · cited by 96
- ConvexOn.isMinOn_of_leftDeriv_nonpos_of_rightDeriv_nonnegproof · cited by 2
- ConvexOn.leftDeriv_le_rightDeriv_of_mem_interiorproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- InformationTheory.isMinOn_klFunproof · cited by 2