Theorems · Theorem · global analysis

HasLineDerivAt.tendsto_slope_zero_right

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {E : Type u_3} [inst_3 : AddCommGroup E] [inst_4 : Module 𝕜 E] {f : E → F} {f' : F}
  {x v : E} [inst_5 : Preorder 𝕜],
  HasLineDerivAt 𝕜 f f' x v → Filter.Tendsto (fun t => t⁻¹ • (f (x + t • v) - f x)) (nhdsWithin 0 (Set.Ioi 0)) (nhds f')

Defined in

Mathlib.Analysis.Calculus.LineDeriv.Basic

Cited by

2 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceAddCommGroupModulePreorder