eventually_nhdsWithin_sign_eq_of_deriv_neg

∀ {f : ℝ → ℝ} {x₀ : ℝ}, deriv f x₀ < 0 → f x₀ = 0 → ∀ᶠ (x : ℝ) in nhds x₀, SignType.sign (f x) = SignType.sign (x₀ - x)

If the derivative of f is negative at a root x₀ of f, then locally the sign of f x matches x₀ - x.

Defined in: Mathlib.Analysis.Calculus.DerivativeTest
Cited by: 0 results in Mathlib
Foundations: Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound

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