2x-4x^(-1/3)

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Solution for 2x-4x^(-1/3) equation:


D( x )

x = 0

x = 0

x = 0

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

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

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

t_1 = x^(1/3)

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

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

1*t_1^4 = 2 // : 1

t_1^4 = 2

t_1^4 = 2 // ^ 1/4

abs(t_1) = 2^(1/4)

t_1 = 2^(1/4) or t_1 = -2^(1/4)

2/t_1 = 0

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

t_1^-1 = 0

t_1 należy do O

t_1 = 2^(1/4)

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

1*x^(1/3) = 2^(1/4) // : 1

x^(1/3) = 2^(1/4)

x^(1/3) = 2^(1/4) // ^ 3

x = 2^(3/4)

t_1 = -2^(1/4)

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

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

x^(1/3) = -2^(1/4)

( -2^(1/4) < 0 i 1/3 in (0:1) ) => x należy do O

x = 2^(3/4)

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