Question

Найти наибольшее и наименьшее значение функции y= x^3 - 6x на отрезке [-3;4]

Answer 1

$y'=3x^2-6, \ y'=0, 3x^2-6=0, \ x^2=2, \ x_1=-sqrt{2}, x_2=sqrt{2}, \ \ x=-3, y=(-3)^3-6cdot(-3)=-9, \ x=-sqrt{2}, y=(-sqrt{2})^3-6cdot(-sqrt{2})=4sqrt{2}, \ x=sqrt{2}, y=(sqrt{2})^3-6sqrt{2}=-4sqrt{2}, \ x=4, y=4^3-6cdot4=40, \ \ minlimits_{xin[-3;4]}y=-9, \ maxlimits_{xin[-3;4]}y=40.$