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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
(1/2)*(9-(3*x)) = 3-(3/x) // - 3-(3/x)
(1/2)*(9-(3*x))+3/x-3 = 0
(1/2)*(9-3*x)+3/x-3 = 0
1/2*(9-3*x)+3/x-3 = 0
(1/2*x*(9-3*x))/x+3/x+(-3*x)/x = 0
1/2*x*(9-3*x)-3*x+3 = 0
9/2*x-3/2*x^2-3*x+3 = 0
3/2*x-3/2*x^2+3 = 0
3/2*x-3/2*x^2+3 = 0
3*(1/2*x-1/2*x^2+1) = 0
1/2*x-1/2*x^2+1 = 0
DELTA = (1/2)^2-(-1/2*1*4)
DELTA = 9/4
DELTA > 0
x = ((9/4)^(1/2)-1/2)/(-1/2*2) or x = (-(9/4)^(1/2)-1/2)/(-1/2*2)
x = -1 or x = 2
3*(x+1)*(x-2) = 0
(3*(x+1)*(x-2))/x = 0
(3*(x+1)*(x-2))/x = 0 // * x
3*(x+1)*(x-2) = 0
( 3 )
3 = 0
x belongs to the empty set
( x+1 )
x+1 = 0 // - 1
x = -1
( x-2 )
x-2 = 0 // + 2
x = 2
x in { -1, 2 }
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