Theorems · Theorem · real analysis
IsLocalExtr.lineDeriv_eq_zero
∀ {E : Type u_1} [inst : AddCommGroup E] [inst_1 : Module ℝ E] [inst_2 : TopologicalSpace E] [ContinuousAdd E]
[ContinuousSMul ℝ E] {f : E → ℝ} {a : E}, IsLocalExtr f a → lineDeriv ℝ f a = 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- add_zeroproof · cited by 2,707
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddstatement and proof · cited by 777
- zero_smulproof · cited by 716
- continuous_id'proof · cited by 295
- continuous_constproof · cited by 278
- Continuous.tendsto'proof · cited by 53
- Continuous.fun_smulproof · cited by 44
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalMax.lineDeriv_eq_zeroproof · cited by 0
- IsLocalMin.lineDeriv_eq_zeroproof · cited by 0