diffContOnCl — Mathlib

English

If the second derivative at x0 is negative and f'(x0)=0 and f is continuous at x0, then x0 is a local maximum.

Русский

Если в точке x0 вторая производная отрицательна и f'(x0)=0, то x0 — локальный максимум.

LaTeX

$$$$\\text{If } f''(x_0)<0,\\ f'(x_0)=0,\\text{ and } f\\text{ is continuous at } x_0,\\ text{ then } x_0\\text{ is a local maximum.}$$$$

Lean4

theorem diffContOnCl (h : DifferentiableOn 𝕜 f (closure s)) : DiffContOnCl 𝕜 f s :=
  ⟨h.mono subset_closure, h.continuousOn⟩

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