t^(-1/2)-16t^(-5/2)

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Solution for t^(-1/2)-16t^(-5/2) equation:


D( t )

t < 0

t = 0

t < 0

t = 0

t = 0

t in (0:+oo)

t^(-1/2)-(16*t^(-5/2)) = 0

t^(-1/2)-16*t^(-5/2) = 0

t_1 = t^(-1/2)

1*t_1^1-16*t_1^5 = 0

t_1-16*t_1^5 = 0

t_1*(1-16*t_1^4) = 0

-16*t_1^4 = -1 // : -16

t_1^4 = 1/16

t_1^4 = 1/16 // ^ 1/4

abs(t_1) = 1/2

t_1 = 1/2 or t_1 = -1/2

t_1 = 0

t_1 = 0

t_1 = 1/2

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

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

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

-1/2 < 0

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

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

2 = t^(1/2)

t^(1/2) = 2 // ^ 2

t = 4

t_1 = -1/2

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

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

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

-1/2 < 0

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

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

-2 = t^(1/2)

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

t = 4

t_1 = 0

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

t^(-1/2) = 0

1*t^(-1/2) = 0 // : 1

t^(-1/2) = 0

t należy do O

t in { 4, 4 }

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