1/2x^-1/2-1/2x^-3/2

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Solution for 1/2x^-1/2-1/2x^-3/2 equation: 


D( x )

x = 0

x = 0

x = 0

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

((1/2)*x^-1)/2-(((1/2)*x^-3)/2) = 0

((1/2)*x^-1)/2+(-1/4)*x^-3 = 0

1/4*x^-1-1/4*x^-3 = 0

t_1 = x^-1

1/4*t_1^1-1/4*t_1^3 = 0

1/4*t_1-1/4*t_1^3 = 0

1/4*t_1*(1-t_1^2) = 0

-1*t_1^2 = -1 // : -1

t_1^2 = 1

t_1^2 = 1 // ^ 1/2

abs(t_1) = 1

t_1 = 1 or t_1 = -1

t_1/4 = 0

1/4*t_1 = 0 // : 1/4

t_1 = 0

t_1 = 1

x^-1-1 = 0

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

x^-1 = 1

-1 < 0

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

1 = 1*x^1 // : 1

1 = x^1

x = 1

t_1 = -1

x^-1+1 = 0

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

x^-1 = -1

-1 < 0

1/(x^1) = -1 // * x^1

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

-1 = x^1

x = -1

t_1 = 0

x^-1+0 = 0

x^-1 = 0

1*x^-1 = 0 // : 1

x^-1 = 0

x należy do O

x in { 1, -1 }

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