Theorems · Theorem · real analysis
IsLocalMax.hasFDerivAt_eq_zero
∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : E → ℝ} {f' : StrongDual ℝ E} {a : E},
IsLocalMax f a → HasFDerivAt f f' a → f' = 0Fermat's Theorem: the derivative of a function at a local maximum equals zero.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- StrongDualstatement and proof · cited by 459
- HasFDerivAtstatement and proof · cited by 350
- neg_eq_zeroproof · cited by 171
- IsLocalMaxstatement and proof · cited by 50
- HasFDerivAt.negproof · cited by 6
- IsLocalMin.hasFDerivAt_eq_zeroproof · cited by 4
- IsLocalMax.negproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalMax.fderiv_eq_zeroproof · cited by 2
- IsLocalExtr.hasFDerivAt_eq_zeroproof · cited by 0