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D( x )
x+6 = 0
x+6 = 0
x+6 = 0
x+6 = 0 // - 6
x = -6
x in (-oo:-6) U (-6:+oo)
(X^3+3*x^2-(11*x)+4)/(x+6) = 0
(X^3+3*x^2-11*x+4)/(x+6) = 0
X^3+3*x^2-11*x+4 = 0
DELTA = (-11)^2-(3*4*(X^3+4))
DELTA = 121-12*(X^3+4)
121-12*(X^3+4) = 0
121-12*(X^3+4) = 0
73-12*X^3 = 0
73-12*X^3 = 0
-12*X^3 = -73 // : -12
X^3 = 73/12
X^3 = 73/12 // ^ 1/3
X = (73/12)^(1/3)
DELTA = 0 <=> t_2 = (73/12)^(1/3)
x = 11/(2*3) i X = (73/12)^(1/3)
x = 11/6 i X = (73/12)^(1/3)
( x = ((121-12*(X^3+4))^(1/2)+11)/(2*3) or x = (11-(121-12*(X^3+4))^(1/2))/(2*3) ) i X > (73/12)^(1/3)
( x = ((121-12*(X^3+4))^(1/2)+11)/6 or x = (11-(121-12*(X^3+4))^(1/2))/6 ) i X > (73/12)^(1/3)
X-(73/12)^(1/3) > 0
X-(73/12)^(1/3) > 0 // + (73/12)^(1/3)
X > (73/12)^(1/3)
x in { 11/6, ((121-12*(X^3+4))^(1/2)+11)/6, (11-(121-12*(X^3+4))^(1/2))/6 }
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