F(x) = 4sin^2 x - 4sin x
f'(x) = 4*2sin x*cos x - 4cos x = 4cos x*(2sin x - 1) = 0
1) cos x = 0;
x1 = pi/2 + 2pi*k; f(x1) = 4sin^2 (pi/2) - 4sin (pi/2) = 4*1 - 4*1 = 0
x2 = -pi/2 + 2pi*k; f(x2) = 4sin^2 (-pi/2) - 4sin (-pi/2) = 4*1 - 4(-1) = 8
2) 2sin x = 1
sin x = 1/2
x3 = pi/6 + 2pi*k; f(x3) = 4*(1/2)^2 - 4*1/2 = 4*1/4 - 4/2 = 1 - 2 = -1
x4 = 5pi/6 + 2pi*k; f(x4) = 4*(1/2)^2 - 4*1/2 = 4*1/4 - 4/2 = 1 - 2 = -1
Разность между наибольшим и наименьшим значениями
8 - (-1) = 9