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D( x )
x = 0
(3*x^2-4)/x <= 0
x = 0
x = 0
(3*x^2-4)/x <= 0
(3*x^2-4)/x <= 0
( 3*x^2-4 )
3*x^2 <= 4
3*x^2 <= 4 // : 3
x^2 <= 4/3
x^2 <= 4/3 // ^ 1/2
abs(x) <= (4/3)^(1/2)
x in <-(4/3)^(1/2):(4/3)^(1/2)>
( x )
x+0 <= 0 // - 0
x <= 0
(-oo:-(4/3)^(1/2)) (-(4/3)^(1/2):0) (0:(4/3)^(1/2)) ((4/3)^(1/2):+oo) 3*x^2-4 + - - + x - - + +
x in (-(4/3)^(1/2):0) U ((4/3)^(1/2):+oo)
ln((3*x^2-4)/x) = 0
ln((3*x^2-4)/x) = ln(e^0)
(3*x^2-4)/x = e^0
(3*x^2-4)/x-e^0 = 0
(3*x^2-4)/x-1 = 0
(3*x^2-4)/x+(-1*x)/x = 0
3*x^2-1*x-4 = 0
3*x^2-x-4 = 0
3*x^2-x-4 = 0
3*x^2-x-4 = 0
DELTA = (-1)^2-(-4*3*4)
DELTA = 49
DELTA > 0
x = (49^(1/2)+1)/(2*3) or x = (1-49^(1/2))/(2*3)
x = 4/3 or x = -1
(x+1)*(x-4/3) = 0
((x+1)*(x-4/3))/x = 0
((x+1)*(x-4/3))/x = 0 // * x
(x+1)*(x-4/3) = 0
( x+1 )
x+1 = 0 // - 1
x = -1
( x-4/3 )
x-4/3 = 0 // + 4/3
x = 4/3
x in { -1, 4/3 }
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