Theorems · Theorem · real analysis
IsLocalMin.hasFDerivAt_eq_zero
∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {f' : StrongDual ℝ E} {a : E},
IsLocalMin f a → HasFDerivAt f f' a → f' = 0Fermat's Theorem: the derivative of a function at a local minimum equals zero.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Set.univproof · cited by 3,945
- StrongDualstatement and proof · cited by 459
- Set.mem_univproof · cited by 416
- HasFDerivAtstatement and proof · cited by 350
- ContinuousLinearMap.extproof · cited by 320
- IsLocalMinstatement and proof · cited by 45
- HasFDerivAt.hasFDerivWithinAtproof · cited by 34
Cited by4
Results whose statement or proof uses this declaration.
- IsLocalMin.hasDerivAt_eq_zeroproof · cited by 4
- IsLocalMax.hasFDerivAt_eq_zeroproof · cited by 2
- IsLocalMin.fderiv_eq_zeroproof · cited by 1
- IsLocalExtr.hasFDerivAt_eq_zeroproof · cited by 0