Theorems · Theorem · real analysis
deriv_pos_left_of_sign_deriv
∀ {f : ℝ → ℝ} {x₀ : ℝ},
(∀ᶠ (x : ℝ) in nhdsWithin x₀ {x₀}ᶜ, SignType.sign (deriv f x) = SignType.sign (x₀ - x)) →
∀ᶠ (b : ℝ) in nhdsWithin x₀ (Set.Iio x₀), deriv f b > 0- Defined in
- Mathlib.Analysis.Calculus.DerivativeTest
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.ofPredproof · cited by 6,101
- Filter.Eventuallystatement and proof · cited by 3,134
- Compl.complstatement and proof · cited by 2,925
- nhdsWithinstatement and proof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- Set.Iiostatement and proof · cited by 1,166
- OrderHomstatement · cited by 934
- derivstatement and proof · cited by 676
Cited by1
Results whose statement or proof uses this declaration.
- isLocalMax_of_sign_derivproof · cited by 1