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İlk olarak kritik noktaların bulunması için gradient'in sıfıra eşitlenmesi, ardından bu noktaların yerel maksimum, yerel minimum veya e noktası olup olmadığını belirlemek için D değerinin hesaplanması ve fxx değerinin incelenmesi anlatılmaktadır. Video, iki kritik noktanın (0,0) yerel minimum ve (1,-1) e noktası olduğu sonucuna varmaktadır."]},"endTime":523,"title":"Çok Değişkenli Fonksiyonların Kritik Noktalarını Bulma ve Sınıflama","beginTime":0}],"fullResult":[{"index":0,"title":"Çok Değişkenli Fonksiyonların Kritik Noktalarını Bulma","list":{"type":"unordered","items":["Video, çok değişkenli fonksiyonların kritik noktalarını bulma ve sınıflama konusunu ele alıyor.","Örnek soruda f(x,y) = 6x² - 2x + 3y² + 6xy fonksiyonunun kritik noktaları bulunup, bu noktaların yerel maksimum, minimum veya e noktası olup olmadığı belirlenecek."]},"beginTime":1,"endTime":32,"href":"/video/preview/6379706272723335036?parent-reqid=1769867056279630-10748046369326804206-balancer-l7leveler-kubr-yp-klg-199-BAL&text=Calculus+Craze&t=1&ask_summarization=1"},{"index":1,"title":"Kritik Noktaların Bulunması","list":{"type":"unordered","items":["Kritik noktaları bulmanın yolu, fonksiyonun gradient'ini (x'e ve y'ye göre kısmi türevlerinden oluşan vektör) sıfıra eşitlemektir.","f'in x'e göre kısmi türevi 12x - 6x² + 6y, y'ye göre kısmi türevi ise 6y + 6x olarak hesaplanır.","Bu türevleri sıfıra eşitleyerek x = 0, x = 1 ve y = 0, y = -1 değerleri bulunur, bu da kritik nokta çiftlerini (0,0), (1,-1) yapar."]},"beginTime":32,"endTime":246,"href":"/video/preview/6379706272723335036?parent-reqid=1769867056279630-10748046369326804206-balancer-l7leveler-kubr-yp-klg-199-BAL&text=Calculus+Craze&t=32&ask_summarization=1"},{"index":2,"title":"Kritik Noktaların Sınıflandırılması","list":{"type":"unordered","items":["Kritik noktaların sınıflandırılması için D = fxx - fyy - fxy² formülü kullanılır.","fxx = 12, fyy = 6, fxy = 6 olarak hesaplanır ve D = 12 - 36 = -24 olarak bulunur.","D = -24 olduğundan, (0,0) noktası yerel minimum, (1,-1) noktası ise e 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