x^(1/2)-10x^(3/2)

Solution for x^(1/2)-10x^(3/2) equation:

D( x )

x < 0

x < 0

x in <0:+oo)

x^(1/2)-(10*x^(3/2)) = 0

x^(1/2)-10*x^(3/2) = 0

t_1 = x^(1/2)

1*t_1^1-10*t_1^3 = 0

t_1-10*t_1^3 = 0

t_1*(1-10*t_1^2) = 0

-10*t_1^2 = -1 // : -10

t_1^2 = 1/10

t_1^2 = 1/10 // ^ 1/2

abs(t_1) = (1/10)^(1/2)

t_1 = (1/10)^(1/2) or t_1 = -(1/10)^(1/2)

t_1 = 0

t_1 = 0

t_1 = (1/10)^(1/2)

x^(1/2)-(1/10)^(1/2) = 0

1*x^(1/2) = (1/10)^(1/2) // : 1

x^(1/2) = (1/10)^(1/2)

x^(1/2) = (1/10)^(1/2) // ^ 2

x = 1/10

t_1 = -(1/10)^(1/2)

x^(1/2)+(1/10)^(1/2) = 0

1*x^(1/2) = -(1/10)^(1/2) // : 1

x^(1/2) = -(1/10)^(1/2)

( -(1/10)^(1/2) < 0 i 1/2 in (0:1) ) => x należy do O

t_1 = 0

x^(1/2)+0 = 0

x^(1/2) = 0

1*x^(1/2) = 0 // : 1

x^(1/2) = 0

x = 0

x in { 1/10, 0 }