Фоменко Т. Н. - Математический анализ. Часть 1 - Лекция 17

The lecture begins with an example of Leibniz's formula (00:00:10), then moves to higher‑order differentials and the non‑invariance of the second differential’s notation (00:05:39). Next, the instructor discusses differentiation of parametrically defined functions (00:22:20), followed by vector functions and their derivatives (00:40:08). The lecture then covers the increase and decrease of a function at a point, including sufficient conditions for monotonicity (00:49:34). It continues with local extrema of functions, necessary conditions for local extrema (01:04:40), and concludes with properties of functions differentiable on an interval, including Rolle’s and Lagrange’s theorems (01:15:21).