Theorems · Theorem · real analysis
IsLocalMin.hasDerivAt_eq_zero
∀ {f : ℝ → ℝ} {f' a : ℝ}, IsLocalMin f a → HasDerivAt 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 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- one_mulproof · cited by 2,841
- HasDerivAtstatement and proof · cited by 493
- DFunLike.congr_funproof · cited by 288
- zero_applyproof · cited by 251
- IsLocalMinstatement and proof · cited by 45
- hasDerivAt_iff_hasFDerivAtproof · cited by 7
- IsLocalMin.hasFDerivAt_eq_zeroproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- IsLocalExtr.hasDerivAt_eq_zeroproof · cited by 3
- exists_hasDerivWithinAt_eq_of_gt_of_ltproof · cited by 2
- IsLocalMax.hasDerivAt_eq_zeroproof · cited by 2
- IsLocalMin.deriv_eq_zeroproof · cited by 1