File: Mathlib/Analysis/Calculus/LocalExtr/LineDeriv.lean

full_name: IsExtrFilter.hasLineDerivAt_eq_zero
code: theorem IsExtrFilter.hasLineDerivAt_eq_zero {l : Filter E} (h : IsExtrFilter f l a)
    (hd : HasLineDerivAt ℝ f f' a b) (h' : Tendsto (fun t : ℝ ↦ a + t • b) (𝓝 0) l) : f' = 0 
goal: f' = 0

full_name: IsExtrFilter.lineDeriv_eq_zero
code: theorem IsExtrFilter.lineDeriv_eq_zero {l : Filter E} (h : IsExtrFilter f l a)
    (h' : Tendsto (fun t : ℝ ↦ a + t • b) (𝓝 0) l) : lineDeriv ℝ f a b = 0 
goal: lineDeriv ℝ f a b = 0

full_name: IsExtrOn.hasLineDerivAt_eq_zero
code: theorem IsExtrOn.hasLineDerivAt_eq_zero (h : IsExtrOn f s a) (hd : HasLineDerivAt ℝ f f' a b)
    (h' : ∀ᶠ t : ℝ in 𝓝 0, a + t • b ∈ s) : f' = 0 
goal: f' = 0

full_name: IsExtrOn.lineDeriv_eq_zero
code: theorem IsExtrOn.lineDeriv_eq_zero (h : IsExtrOn f s a) (h' : ∀ᶠ t : ℝ in 𝓝 0, a + t • b ∈ s) :
    lineDeriv ℝ f a b = 0 
goal: lineDeriv ℝ f a b = 0

full_name: IsMinOn.hasLineDerivAt_eq_zero
code: theorem IsMinOn.hasLineDerivAt_eq_zero (h : IsMinOn f s a) (hd : HasLineDerivAt ℝ f f' a b)
    (h' : ∀ᶠ t : ℝ in 𝓝 0, a + t • b ∈ s) : f' = 0 
goal: f' = 0

full_name: IsMinOn.lineDeriv_eq_zero
code: theorem IsMinOn.lineDeriv_eq_zero (h : IsMinOn f s a) (h' : ∀ᶠ t : ℝ in 𝓝 0, a + t • b ∈ s) :
    lineDeriv ℝ f a b = 0 
goal: lineDeriv ℝ f a b = 0

full_name: IsMaxOn.hasLineDerivAt_eq_zero
code: theorem IsMaxOn.hasLineDerivAt_eq_zero (h : IsMaxOn f s a) (hd : HasLineDerivAt ℝ f f' a b)
    (h' : ∀ᶠ t : ℝ in 𝓝 0, a + t • b ∈ s) : f' = 0 
goal: f' = 0

full_name: IsMaxOn.lineDeriv_eq_zero
code: theorem IsMaxOn.lineDeriv_eq_zero (h : IsMaxOn f s a) (h' : ∀ᶠ t : ℝ in 𝓝 0, a + t • b ∈ s) :
    lineDeriv ℝ f a b = 0 
goal: lineDeriv ℝ f a b = 0

full_name: IsExtrOn.hasLineDerivWithinAt_eq_zero
code: theorem IsExtrOn.hasLineDerivWithinAt_eq_zero (h : IsExtrOn f s a)
    (hd : HasLineDerivWithinAt ℝ f f' s a b) (h' : ∀ᶠ t : ℝ in 𝓝 0, a + t • b ∈ s) : f' = 0 
goal: f' = 0

full_name: IsExtrOn.lineDerivWithin_eq_zero
code: theorem IsExtrOn.lineDerivWithin_eq_zero (h : IsExtrOn f s a)
    (h' : ∀ᶠ t : ℝ in 𝓝 0, a + t • b ∈ s) : lineDerivWithin ℝ f s a b = 0 
goal: lineDerivWithin ℝ f s a b = 0

full_name: IsMinOn.hasLineDerivWithinAt_eq_zero
code: theorem IsMinOn.hasLineDerivWithinAt_eq_zero (h : IsMinOn f s a)
    (hd : HasLineDerivWithinAt ℝ f f' s a b) (h' : ∀ᶠ t : ℝ in 𝓝 0, a + t • b ∈ s) : f' = 0 
goal: f' = 0

full_name: IsMinOn.lineDerivWithin_eq_zero
code: theorem IsMinOn.lineDerivWithin_eq_zero (h : IsMinOn f s a)
    (h' : ∀ᶠ t : ℝ in 𝓝 0, a + t • b ∈ s) : lineDerivWithin ℝ f s a b = 0 
goal: lineDerivWithin ℝ f s a b = 0

full_name: IsMaxOn.hasLineDerivWithinAt_eq_zero
code: theorem IsMaxOn.hasLineDerivWithinAt_eq_zero (h : IsMaxOn f s a)
    (hd : HasLineDerivWithinAt ℝ f f' s a b) (h' : ∀ᶠ t : ℝ in 𝓝 0, a + t • b ∈ s) : f' = 0 
goal: f' = 0

full_name: IsMaxOn.lineDerivWithin_eq_zero
code: theorem IsMaxOn.lineDerivWithin_eq_zero (h : IsMaxOn f s a)
    (h' : ∀ᶠ t : ℝ in 𝓝 0, a + t • b ∈ s) : lineDerivWithin ℝ f s a b = 0 
goal: lineDerivWithin ℝ f s a b = 0

full_name: IsLocalExtr.hasLineDerivAt_eq_zero
code: theorem IsLocalExtr.hasLineDerivAt_eq_zero (h : IsLocalExtr f a) (hd : HasLineDerivAt ℝ f f' a b) :
    f' = 0 
goal: f' = 0

full_name: IsLocalExtr.lineDeriv_eq_zero
code: theorem IsLocalExtr.lineDeriv_eq_zero (h : IsLocalExtr f a) : lineDeriv ℝ f a = 0 
goal: lineDeriv ℝ f a = 0

full_name: IsLocalMin.hasLineDerivAt_eq_zero
code: theorem IsLocalMin.hasLineDerivAt_eq_zero (h : IsLocalMin f a) (hd : HasLineDerivAt ℝ f f' a b) :
    f' = 0 
goal: f' = 0

full_name: IsLocalMin.lineDeriv_eq_zero
code: theorem IsLocalMin.lineDeriv_eq_zero (h : IsLocalMin f a) : lineDeriv ℝ f a = 0 
goal: lineDeriv ℝ f a = 0

full_name: IsLocalMax.hasLineDerivAt_eq_zero
code: theorem IsLocalMax.hasLineDerivAt_eq_zero (h : IsLocalMax f a) (hd : HasLineDerivAt ℝ f f' a b) :
    f' = 0 
goal: f' = 0

full_name: IsLocalMax.lineDeriv_eq_zero
code: theorem IsLocalMax.lineDeriv_eq_zero (h : IsLocalMax f a) : lineDeriv ℝ f a = 0 
goal: lineDeriv ℝ f a = 0