6x-384/x^20

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Solution for 6x-384/x^20 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

6*x-(384/(x^2)) > 0

6*x-384*x^-2 > 0

6*x-384*x^-2 = 0

6*x*(1-64*x^-3) = 0

-64*x^-3 = -1 // : -64

x^-3 = 1/64

-3 < 0

1/(x^3) = 1/64 // * x^3

1 = 1/64*x^3 // : 1/64

64 = x^3

x^3 = 64 // ^ 1/3

x = 4

6*x = 0

6*x = 0 // : 6

x = 0

x*(x-4) > 0

	(-oo:0)	(0:4)	(4:+oo)
x-4	-	-	+
x	-	+	+


x in (-oo:0) U (4:+oo)

(-oo:0) U (4:+oo)

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