Theorems · Theorem · real analysis
IsLocalMinOn.fderivWithin_eq_zero
∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {s : Set E} {a y : E},
IsLocalMinOn f s a → y ∈ posTangentConeAt s a → -y ∈ posTangentConeAt s a → (fderivWithin ℝ f s a) y = 0If f has a local min on s at a and both y and -y belong to the positive tangent cone
of s at a, then f' y = 0.
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- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
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