y=(x+2)^2*x-8
y=(x^2+4x+4)*x-8=x^3+4x^2+4x-8
Производная x^3+4x^2+4x-8=3x^2+4*2x+4=3x^2+8x+4
3x^2+8x+4=0
3x2 + 8x + 4 = 0D = b2 - 4acD = 64 - 48 = 16 = 4^2
x1,2 = -b ± √D/2ax1 = -8 + 4/6 = - 4/6 = - 2/3x2 = -8 - 4/6 = - 12/6= -2ответ: x1 = - 2/3 ; x2 = -2
x min=-2 y min=-8
x max=-2/3 y max=-4
y=(x+2)^2*x-8
y=(x^2+4x+4)*x-8=x^3+4x^2+4x-8
Производная x^3+4x^2+4x-8=3x^2+4*2x+4=3x^2+8x+4
3x^2+8x+4=0
3x2 + 8x + 4 = 0
D = b2 - 4ac
D = 64 - 48 = 16 = 4^2
x1,2 = -b ± √D/2a
x1 = -8 + 4/6 = - 4/6 = - 2/3
x2 = -8 - 4/6 = - 12/6= -2
ответ: x1 = - 2/3 ; x2 = -2
x min=-2 y min=-8
x max=-2/3 y max=-4