Theorems · Theorem · real analysis
IsLocalMax.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}, IsLocalMax f a → lineDeriv ℝ f a = 0- Cited by
- 0 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddstatement and proof · cited by 777
- IsLocalMaxstatement and proof · cited by 50
- lineDerivstatement · cited by 43
- IsLocalExtr.lineDeriv_eq_zeroproof · cited by 2
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