Question

Знайдiть найменшим значения функцii y=9x-x^3/3 на промiжку [-1;0]

Answer 1

$y=9x- \frac{x^3}{3} \\ \\ y'=9- \frac{3x^2}{3} \\ \\ y'=9-x^2 \\ \\ y'=0 \\ \\ 9-x^2=0 \\ \\ (3-x)(3+x)=0 \\ \\ -----[-3]+++++[3]----- \\ \\ x_{min}=-3 \\ \\ f(-3)=-27+9=-18 \\ \\ f(0)=0 \\ \\ f(-1)=-9+ \frac{1}{3} =- \frac{26}{3} \\ \\ f_{min}=- \frac{26}{3}$