KO’P O’ZGARUVCHILI FUNKSIYALARNING EKSTREMUMLARI
Keywords:
ko‘p o‘zgaruvchili funksiya, ekstremum, lokal maksimum, lokal minimum, global ekstremum, stasionar nuqta, kritik nuqta, gradient, gessian, Hesse matritsasi, ikkinchi tartibli hosila, cheklovli ekstremum, Lagrange usuli, optimallashtirish, funksiyaning differensiallanuvchanligi, egilish nuqtasi, chegaraviy ekstremum.Abstract
Ushbu mavzuda ko‘p o‘zgaruvchili funksiyalarning lokal va global ekstremumlarini aniqlashga oid nazariy va amaliy masalalar yoritiladi. Avvalo, ikki va undan ortiq o‘zgaruvchili funksiyalarning differensiallanish shartlari, gradient, gessian (Hesse matritsasi) tushunchalari keltiriladi. Keyinchalik ekstremum mavjudligi uchun zarur va yetarli shartlar, xususan, stasionar nuqtalarni topish, ikkinchi tartibli hosilalar yordamida nuqtaning turi (minimum, maksimum yoki egilish nuqtasi)ni aniqlash usullari izohlanadi.
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