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

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


D( x )

x = 0

x = 0

x = 0

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

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

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

1/2*x^-1-1/4*x^-3 = 0

t_1 = x^-1

1/2*t_1^1-1/4*t_1^3 = 0

1/2*t_1-1/4*t_1^3 = 0

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

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

t_1^2 = 2

t_1^2 = 2 // ^ 1/2

abs(t_1) = 2^(1/2)

t_1 = 2^(1/2) or t_1 = -2^(1/2)

t_1/2 = 0

1/2*t_1 = 0 // : 1/2

t_1 = 0

t_1 = 2^(1/2)

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

1*x^-1 = 2^(1/2) // : 1

x^-1 = 2^(1/2)

-1 < 0

1/(x^1) = 2^(1/2) // * x^1

1 = 2^(1/2)*x^1 // : 2^(1/2)

1/(2^(1/2)) = x^1

x = 1/(2^(1/2))

t_1 = -2^(1/2)

x^-1+2^(1/2) = 0

1*x^-1 = -2^(1/2) // : 1

x^-1 = -2^(1/2)

-1 < 0

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

1 = -2^(1/2)*x^1 // : -2^(1/2)

1/(-2^(1/2)) = x^1

x = 1/(2^(1/2))

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/(2^(1/2)), 1/(2^(1/2)) }

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