Theorems · Theorem · real analysis
exists_deriv_eq_zero
- 1000+ list: Rolle's theorem
∀ {f : ℝ → ℝ} {a b : ℝ}, a < b → ContinuousOn f (Set.Icc a b) → f a = f b → ∃ c ∈ Set.Ioo a b, deriv f c = 0Rolle's Theorem deriv version
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 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 · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.Iccstatement and proof · cited by 1,702
- ContinuousOnstatement and proof · cited by 1,411
- Set.Ioostatement and proof · cited by 1,214
- derivstatement and proof · cited by 676
- IsLocalExtrproof · cited by 28
- exists_isLocalExtr_Iooproof · cited by 3
- IsLocalExtr.deriv_eq_zeroproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.card_roots_toFinset_le_card_roots_derivative_sdiff_roots_succproof · cited by 3