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D( x )
3*x+1 = 0
3*x+1 = 0
3*x+1 = 0
3*x+1 = 0 // - 1
3*x = -1 // : 3
x = -1/3
x in (-oo:-1/3) U (-1/3:+oo)
(6*x^3-x^2+11*x+4)/(3*x+1) = 0
6*x^3-x^2+11*x+4 = 0
6*x^3-x^2+11*x+4 = 0
{ 1, -1, 2, -2, 4, -4 }
1
x = 1
6*x^3-x^2+11*x+4 = 20
1
-1
x = -1
6*x^3-x^2+11*x+4 = -14
-1
2
x = 2
6*x^3-x^2+11*x+4 = 70
2
-2
x = -2
6*x^3-x^2+11*x+4 = -70
-2
4
x = 4
6*x^3-x^2+11*x+4 = 416
4
-4
x = -4
6*x^3-x^2+11*x+4 = -440
-4
{ 1/2, -1/2, 1/3, -1/3, 1/6, -1/6, -1/2, 1/2, -1/3, 1/3, -1/6, 1/6, 2/2, -2/2, 2/3, -2/3, 2/6, -2/6, -2/2, 2/2, -2/3, 2/3, -2/6, 2/6, 4/2, -4/2, 4/3, -4/3, 4/6, -4/6, -4/2, 4/2, -4/3, 4/3, -4/6, 4/6 }
1/2
x
1/2
6*x^3-x^2+11*x+4 = 10
1/2
-1/2
x
-1/2
6*x^3-x^2+11*x+4 = -2.5
-1/2
1/3
x
1/3
6*x^3-x^2+11*x+4 = 7.77777778
1/3
-1/3
x
-1/3
6*x^3-x^2+11*x+4 = 0
-1/3
x+1/3
6*x^2-3*x+12
6*x^3-x^2+11*x+4
x+1/3
-6*x^3-2*x^2
11*x-3*x^2+4
3*x^2+x
12*x+4
-12*x-4
0
6*x^2-3*x+12 = 0
DELTA = (-3)^2-(4*6*12)
DELTA = -279
DELTA < 0
x in { -1/3}
x+1/3 = 0
(x+1/3)/(3*x+1) = 0
x+1/3 = 0 // - 1/3
x = -1/3
x in { -1/3}
x belongs to the empty set
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