eventually_nhdsWithin_sign_eq_of_deriv_pos

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

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

Defined in: Mathlib.Analysis.Calculus.DerivativeTest
Cited by: 2 results in Mathlib
Foundations: Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

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