Предмет: Алгебра, автор: doll93391

Найдите точку максимума функции y=6 15x-4x*корень из х

Korgath: Между 6 и 15х что стоит?

Korgath: Допустим, что плюс... ))

Ответы

Автор ответа: Korgath

12

$y=-4x^{ \frac{3}{2} }+ 15x+6\\y'=-6 \sqrt{x} +15\\$

Экстремумы - при производной равной 0

$-6 \sqrt{x} +15=0\\ \sqrt{x} =5/2\\x=25/4=6,25\\ y=6+15*6,25-4*6,25^{1,5}= 6+93,75-62,5=37,25.\\(6,25;37,25)$

при x=0, y=6, при x=7, y = 37 значит найденная точка - максимум.

график функции привел для наглядности... ))

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