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D( x )
x-2 = 0
x-2 = 0
x-2 = 0
x-2 = 0 // + 2
x = 2
x in (-oo:2) U (2:+oo)
(X^3-(3*x^2)+8*x+11)/(x-2) = 0
(X^3-3*x^2+8*x+11)/(x-2) = 0
X^3-3*x^2+8*x+11 = 0
DELTA = 8^2-(-3*4*(X^3+11))
DELTA = 12*(X^3+11)+64
12*(X^3+11)+64 = 0
12*(X^3+11)+64 = 0
12*X^3+196 = 0
12*X^3+196 = 0
12*X^3 = -196 // : 12
X^3 = -49/3
X^3 = -49/3 // ^ 1/3
X = -(49/3)^(1/3)
DELTA = 0 <=> t_2 = -(49/3)^(1/3)
x = -8/(-3*2) i X = -(49/3)^(1/3)
x = 4/3 i X = -(49/3)^(1/3)
( x = ((12*(X^3+11)+64)^(1/2)-8)/(-3*2) or x = (-(12*(X^3+11)+64)^(1/2)-8)/(-3*2) ) i X > -(49/3)^(1/3)
( x = ((12*(X^3+11)+64)^(1/2)-8)/(-6) or x = ((12*(X^3+11)+64)^(1/2)+8)/6 ) i X > -(49/3)^(1/3)
X+(49/3)^(1/3) > 0
X+(49/3)^(1/3) > 0 // - (49/3)^(1/3)
X > -(49/3)^(1/3)
x in { 4/3, ((12*(X^3+11)+64)^(1/2)-8)/(-6), ((12*(X^3+11)+64)^(1/2)+8)/6 }
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