Theorems · Theorem · real analysis
IsLocalMin.deriv_eq_zero
∀ {f : ℝ → ℝ} {a : ℝ}, IsLocalMin f a → deriv f a = 0Fermat's Theorem: the derivative of a function at a local minimum equals zero.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- derivstatement · cited by 676
- DifferentiableAtproof · cited by 617
- DifferentiableAt.hasDerivAtproof · cited by 114
- IsLocalMinstatement and proof · cited by 45
- deriv_zero_of_not_differentiableAtproof · cited by 34
- IsLocalMin.hasDerivAt_eq_zeroproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalExtr.deriv_eq_zeroproof · cited by 2