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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
3*x-(6/x) > -17 // + 17
3*x-(6/x)+17 > 0
3*x-6*x^-1+17 > 0
3*x-6*x^-1+17 = 0
3*x^1-6*x^-1+17*x^0 = 0
(3*x^2+17*x^1-6*x^0)/(x^1) = 0 // * x^2
x^1*(3*x^2+17*x^1-6*x^0) = 0
x^1
3*x^2+17*x-6 = 0
3*x^2+17*x-6 = 0
DELTA = 17^2-(-6*3*4)
DELTA = 361
DELTA > 0
x = (361^(1/2)-17)/(2*3) or x = (-361^(1/2)-17)/(2*3)
x = 1/3 or x = -6
x in { -6, 1/3}
(x+6)*(x-1/3) > 0
(-oo:-6) (-6:1/3) (1/3:+oo) x+6 - + + x-1/3 - - +
x in (-oo:-6) U (1/3:+oo)
(-oo:-6) U (1/3:+oo)
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