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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
24*x-2 > 15/x // - 15/x
24*x-(15/x)-2 > 0
24*x-15*x^-1-2 > 0
24*x-15*x^-1-2 = 0
24*x^1-15*x^-1-2*x^0 = 0
(24*x^2-2*x^1-15*x^0)/(x^1) = 0 // * x^2
x^1*(24*x^2-2*x^1-15*x^0) = 0
x^1
24*x^2-2*x-15 = 0
24*x^2-2*x-15 = 0
DELTA = (-2)^2-(-15*4*24)
DELTA = 1444
DELTA > 0
x = (1444^(1/2)+2)/(2*24) or x = (2-1444^(1/2))/(2*24)
x = 5/6 or x = -3/4
x in { -3/4, 5/6}
(x+3/4)*(x-5/6) > 0
(-oo:-3/4) (-3/4:5/6) (5/6:+oo) x+3/4 - + + x-5/6 - - +
x in (-oo:-3/4) U (5/6:+oo)
(-oo:-3/4) U (5/6:+oo)
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