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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
192 = 2*(x-4)*(200/x-4) // - 2*(x-4)*(200/x-4)
192-(2*(x-4)*(200/x-4)) = 0
192-2*(x-4)*(200/x-4) = 0
192-2*(x-4)*(200*x^-1-4) = 0
192-2*(x-4)*(200*x^-1-4) = 0
8*x+1600*x^-1-240 = 0
8*x+1600*x^-1-240 = 0
8*(x+200*x^-1-30) = 0
1*x^1+200*x^-1-30*x^0 = 0
(1*x^2-30*x^1+200*x^0)/(x^1) = 0 // * x^2
x^1*(1*x^2-30*x^1+200*x^0) = 0
x^1
x^2-30*x+200 = 0
x^2-30*x+200 = 0
DELTA = (-30)^2-(1*4*200)
DELTA = 100
DELTA > 0
x = (100^(1/2)+30)/(1*2) or x = (30-100^(1/2))/(1*2)
x = 20 or x = 10
x in { 10, 20}
8*(x-10)*(x-20) = 0
8*(x-10)*(x-20) = 0
( 8 )
8 = 0
x belongs to the empty set
( x-10 )
x-10 = 0 // + 10
x = 10
( x-20 )
x-20 = 0 // + 20
x = 20
x in { 10, 20 }
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