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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
(x-(8/x))^2+9*x-(72/x)+14 = 0
(x-8*x^-1)^2+9*x-72*x^-1+14 = 0
(x-8*x^-1)^2+9*x-72/x+14 = 0
(x*(x-8*x^-1)^2)/x+(9*x*x)/x-72/x+(14*x)/x = 0
x*(x-8*x^-1)^2+9*x*x+14*x-72 = 0
x^3+9*x^2-16*x+14*x+64*x^-1-72 = 0
x^3+9*x^2-2*x+64*x^-1-72 = 0
x^3+9*x^2-2*x+64*x^-1-72 = 0
1*x^3+9*x^2-2*x^1+64*x^-1-72*x^0 = 0
(1*x^4+9*x^3-2*x^2-72*x^1+64*x^0)/(x^1) = 0 // * x^2
x^1*(1*x^4+9*x^3-2*x^2-72*x^1+64*x^0) = 0
x^1
x^4+9*x^3-2*x^2-72*x+64 = 0
{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64 }
1
x = 1
x^4+9*x^3-2*x^2-72*x+64 = 0
1
x-1
x^3+10*x^2+8*x-64
x^4+9*x^3-2*x^2-72*x+64
x-1
x^3-x^4
10*x^3-2*x^2-72*x+64
10*x^2-10*x^3
8*x^2-72*x+64
8*x-8*x^2
64-64*x
64*x-64
0
x^3+10*x^2+8*x-64 = 0
{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64 }
1
x = 1
x^3+10*x^2+8*x-64 = -45
1
-1
x = -1
x^3+10*x^2+8*x-64 = -63
-1
2
x = 2
x^3+10*x^2+8*x-64 = 0
2
x-2
x^2+12*x+32
x^3+10*x^2+8*x-64
x-2
2*x^2-x^3
12*x^2+8*x-64
24*x-12*x^2
32*x-64
64-32*x
0
x^2+12*x+32 = 0
DELTA = 12^2-(1*4*32)
DELTA = 16
DELTA > 0
x = (16^(1/2)-12)/(1*2) or x = (-16^(1/2)-12)/(1*2)
x = -4 or x = -8
x in { -8, -4, 1, 2}
(x+8)*(x+4)*(x-1)*(x-2) = 0
((x+8)*(x+4)*(x-1)*(x-2))/x = 0
((x+8)*(x+4)*(x-1)*(x-2))/x = 0 // * x
(x+8)*(x+4)*(x-1)*(x-2) = 0
( x+4 )
x+4 = 0 // - 4
x = -4
( x+8 )
x+8 = 0 // - 8
x = -8
( x-1 )
x-1 = 0 // + 1
x = 1
( x-2 )
x-2 = 0 // + 2
x = 2
x in { -4, -8, 1, 2 }
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