Theorems · Theorem · real analysis
isLocalMax_of_deriv_deriv_neg
∀ {f : ℝ → ℝ} {x₀ : ℝ}, deriv (deriv f) x₀ < 0 → deriv f x₀ = 0 → ContinuousAt f x₀ → IsLocalMax f x₀The Second-Derivative Test from calculus, maximum version.
- Defined in
- Mathlib.Analysis.Calculus.DerivativeTest
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- neg_negproof · cited by 960
- ContinuousAtstatement and proof · cited by 697
- derivstatement and proof · cited by 676
- IsLocalMaxstatement and proof · cited by 50
- deriv.fun_neg'proof · cited by 8
- deriv.neg'proof · cited by 8
- ContinuousAt.negproof · cited by 6
- IsLocalMin.negproof · cited by 1
- isLocalMin_of_deriv_deriv_posproof · cited by 1
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