Question

Найдите точку максимума функции y=-9x^2-x^3+12.

Answer 1

$f(x)=-9x^2-x^3+12\\\\f'(x)=-18x-3x^2\\\\f'(x)=0:\\\\-18x-3x^2=0\ \ \mid \div3\\\\-6x-x^2=0\\\\6x+x^2=0\\\\x(6+x)=0\\\\x=0\\x=-6\\\\-----[-6]+++++[0]-----\\\\x_{max}=0\\\\f_{max}=f(x_{max})=-9*0^2-0^3+12=12\\\\(x;y)=(0;12)$