Theorems · Theorem · real analysis

hasDerivAt_iff_tendsto_slope_zero

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {x : 𝕜},
  HasDerivAt f f' x ↔ Filter.Tendsto (fun t => t⁻¹ • (f (x + t) - f x)) (nhdsWithin 0 {0}ᶜ) (nhds f')

Defined in

Mathlib.Analysis.Calculus.Deriv.Slope

Cited by

1 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace