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türevi S' = 2x - 576/x³ olarak bulunuyor ve bu türev sıfır eşitlenerek x = ±4 değerleri elde ediliyor.","x = 4 için y = -4, x = -4 için y = 4 olduğu görülüyor, bu iki sayı çarpımları -16 olan ve karelerinin toplamı minimum olan sayılar."]},"beginTime":103,"endTime":309,"href":"/video/preview/15337069700319503372?parent-reqid=1769052458230735-10330783406312877040-balancer-l7leveler-kubr-yp-klg-78-BAL&text=Calcus.com&t=103&ask_summarization=1"},{"index":2,"title":"Minimum Değerin İspatı","list":{"type":"unordered","items":["Fonksiyonun ikinci türevi S'' = 2 + 1536/x⁴ olarak bulunuyor ve x = 4 için S'' pozitif olduğu görüldüğü için minimum noktası olduğu ispatlanıyor.","x = 4 için karelerinin toplamı S(4) = 4² + (-4)² = 32 olarak hesaplanıyor.","Diğer çarpımları -16 olan sayı çiftleri (1 ve -16, -8 ve 2 gibi) için karelerinin toplamı 32'den büyük olduğu gösteriliyor."]},"beginTime":309,"endTime":456,"href":"/video/preview/15337069700319503372?parent-reqid=1769052458230735-10330783406312877040-balancer-l7leveler-kubr-yp-klg-78-BAL&text=Calcus.com&t=309&ask_summarization=1"}],"linkTemplate":"/video/preview/15337069700319503372?parent-reqid=1769052458230735-10330783406312877040-balancer-l7leveler-kubr-yp-klg-78-BAL&text=Calcus.com&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Kalkülüs ile Optimizasyon Hesaplaması 1 (Kalkülüs / Türev 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