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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
3*(4*x-(1/x))^2-(4*(4*x-(1/x)))-15 = 0
3*(4*x-x^-1)^2-4*(4*x-x^-1)-15 = 0
3*(4*x-x^-1)^2-4*(4*x-x^-1)-15 = 0
48*x^2-16*x+4*x^-1+3*x^-2-24-15 = 0
48*x^2-16*x+4*x^-1+3*x^-2-39 = 0
48*x^2-16*x+4*x^-1+3*x^-2-39 = 0
48*x^2-16*x^1+4*x^-1+3*x^-2-39*x^0 = 0
(48*x^4-16*x^3-39*x^2+4*x^1+3*x^0)/(x^2) = 0 // * x^4
x^2*(48*x^4-16*x^3-39*x^2+4*x^1+3*x^0) = 0
x^2
48*x^4-16*x^3-39*x^2+4*x+3 = 0
{ 1, -1, 3, -3 }
1
x = 1
48*x^4-16*x^3-39*x^2+4*x+3 = 0
1
x-1
48*x^3+32*x^2-7*x-3
48*x^4-16*x^3-39*x^2+4*x+3
x-1
48*x^3-48*x^4
32*x^3-39*x^2+4*x+3
32*x^2-32*x^3
4*x-7*x^2+3
7*x^2-7*x
3-3*x
3*x-3
0
48*x^3+32*x^2-7*x-3 = 0
{ 1, -1, 3, -3 }
1
x = 1
48*x^3+32*x^2-7*x-3 = 70
1
-1
x = -1
48*x^3+32*x^2-7*x-3 = -12
-1
3
x = 3
48*x^3+32*x^2-7*x-3 = 1560
3
-3
x = -3
48*x^3+32*x^2-7*x-3 = -990
-3
{ 1/2, -1/2, 1/3, -1/3, 1/4, -1/4, 1/6, -1/6, 1/8, -1/8, 1/12, -1/12, 1/16, -1/16, 1/24, -1/24, 1/48, -1/48, -1/2, 1/2, -1/3, 1/3, -1/4, 1/4, -1/6, 1/6, -1/8, 1/8, -1/12, 1/12, -1/16, 1/16, -1/24, 1/24, -1/48, 1/48, 3/2, -3/2, 3/3, -3/3, 3/4, -3/4, 3/6, -3/6, 3/8, -3/8, 3/12, -3/12, 3/16, -3/16, 3/24, -3/24, 3/48, -3/48, -3/2, 3/2, -3/3, 3/3, -3/4, 3/4, -3/6, 3/6, -3/8, 3/8, -3/12, 3/12, -3/16, 3/16, -3/24, 3/24, -3/48, 3/48 }
1/2
x
1/2
48*x^3+32*x^2-7*x-3 = 7.5
1/2
-1/2
x
-1/2
48*x^3+32*x^2-7*x-3 = 2.5
-1/2
1/3
x
1/3
48*x^3+32*x^2-7*x-3 = 0.00000001
1/3
-1/3
x
-1/3
48*x^3+32*x^2-7*x-3 = 1.11111111
-1/3
1/4
x
1/4
48*x^3+32*x^2-7*x-3 = -2
1/4
-1/4
x
-1/4
48*x^3+32*x^2-7*x-3 = 0
-1/4
x+1/4
48*x^2+20*x-12
48*x^3+32*x^2-7*x-3
x+1/4
-48*x^3-12*x^2
20*x^2-7*x-3
-20*x^2-5*x
-12*x-3
12*x+3
0
48*x^2+20*x-12 = 0
DELTA = 20^2-(-12*4*48)
DELTA = 2704
DELTA > 0
x = (2704^(1/2)-20)/(2*48) or x = (-2704^(1/2)-20)/(2*48)
x = 1/3 or x = -3/4
x in { -3/4, 1/3, 1, -1/4}
(x+3/4)*(x-1/3)*(x-1)*(x+1/4) = 0
(x+3/4)*(x-1/3)*(x-1)*(x+1/4) = 0
( x+1/4 )
x+1/4 = 0 // - 1/4
x = -1/4
( x+3/4 )
x+3/4 = 0 // - 3/4
x = -3/4
( x-1/3 )
x-1/3 = 0 // + 1/3
x = 1/3
( x-1 )
x-1 = 0 // + 1
x = 1
x in { -1/4, -3/4, 1/3, 1 }
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