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D( x )
3*x^3-(18*x^2)+33*x-18 = 0
3*x^3-(18*x^2)+33*x-18 = 0
3*x^3-(18*x^2)+33*x-18 = 0
3*x^3-18*x^2+33*x-18 = 0
3*x^3-18*x^2+33*x-18 = 0
3*(x^3-6*x^2+11*x-6) = 0
x^3-6*x^2+11*x-6 = 0
{ 1, -1, 2, -2, 3, -3, 6, -6 }
1
x = 1
x^3-6*x^2+11*x-6 = 0
1
x-1
x^2-5*x+6
x^3-6*x^2+11*x-6
x-1
x^2-x^3
11*x-5*x^2-6
5*x^2-5*x
6*x-6
6-6*x
0
x^2-5*x+6 = 0
DELTA = (-5)^2-(1*4*6)
DELTA = 1
DELTA > 0
x = (1^(1/2)+5)/(1*2) or x = (5-1^(1/2))/(1*2)
x = 3 or x = 2
x in { 2, 3, 1}
3 = 0
x in (-oo:1) U (1:2) U (2:3) U (3:+oo)
(x^3-(3*x^2)-(4*x)+12)/(3*x^3-(18*x^2)+33*x-18) = 0
(x^3-3*x^2-4*x+12)/(3*x^3-18*x^2+33*x-18) = 0
x^3-3*x^2-4*x+12 = 0
x^3-3*x^2-4*x+12 = 0
{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12 }
1
x = 1
x^3-3*x^2-4*x+12 = 6
1
-1
x = -1
x^3-3*x^2-4*x+12 = 12
-1
2
x = 2
x^3-3*x^2-4*x+12 = 0
2
x-2
x^2-x-6
x^3-3*x^2-4*x+12
x-2
2*x^2-x^3
12-x^2-4*x
x^2-2*x
12-6*x
6*x-12
0
x^2-x-6 = 0
DELTA = (-1)^2-(-6*1*4)
DELTA = 25
DELTA > 0
x = (25^(1/2)+1)/(1*2) or x = (1-25^(1/2))/(1*2)
x = 3 or x = -2
x in { -2, 3, 2}
(x+2)*(x-3)*(x-2) = 0
3*x^3-18*x^2+33*x-18 = 0
3*(x^3-6*x^2+11*x-6) = 0
x^3-6*x^2+11*x-6 = 0
{ 1, -1, 2, -2, 3, -3, 6, -6 }
1
x = 1
x^3-6*x^2+11*x-6 = 0
1
x-1
x^2-5*x+6
x^3-6*x^2+11*x-6
x-1
x^2-x^3
11*x-5*x^2-6
5*x^2-5*x
6*x-6
6-6*x
0
x^2-5*x+6 = 0
DELTA = (-5)^2-(1*4*6)
DELTA = 1
DELTA > 0
x = (1^(1/2)+5)/(1*2) or x = (5-1^(1/2))/(1*2)
x = 3 or x = 2
x in { 2, 3, 1}
3*(x-2)*(x-3)*(x-1) = 0
((x+2)*(x-3)*(x-2))/(3*(x-2)*(x-3)*(x-1)) = 0
( x+2 )
x+2 = 0 // - 2
x = -2
( x-2 )
x-2 = 0 // + 2
x = 2
( x-3 )
x-3 = 0 // + 3
x = 3
x in { 2}
x in { 3}
x = -2
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