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D( x )
(5-x)^2 = 0
(5-x)^2 = 0
(5-x)^2 = 0
5-x = 0 // - 5
-x = -5 // * -1
x = 5
x in (-oo:5) U (5:+oo)
1000*(-8/((5-x)^2))+2000 = 0
(-8*1000)/((5-x)^2)+2000 = 0
(-8*1000)/((5-x)^2)+(2000*(5-x)^2)/((5-x)^2) = 0
2000*(5-x)^2-8*1000 = 0
2000*x^2-20000*x+42000 = 0
2000*x^2-20000*x+42000 = 0
2000*(x^2-10*x+21) = 0
x^2-10*x+21 = 0
DELTA = (-10)^2-(1*4*21)
DELTA = 16
DELTA > 0
x = (16^(1/2)+10)/(1*2) or x = (10-16^(1/2))/(1*2)
x = 7 or x = 3
2000*(x-3)*(x-7) = 0
(2000*(x-3)*(x-7))/((5-x)^2) = 0
(2000*(x-3)*(x-7))/((5-x)^2) = 0 // * (5-x)^2
2000*(x-3)*(x-7) = 0
( x-3 )
x-3 = 0 // + 3
x = 3
( x-7 )
x-7 = 0 // + 7
x = 7
x in { 3, 7 }
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