The function `f(x)=(2x^2-1)/x^4, x gt 0`decreases in the interval

Explanation

The function f(x)`=(2x^(2)-1)/(x^(4))`, where `x gt 0`, decreases in the interval `(1,infty)`
`therefore f^(')(x) = (x^(4).4x-(2x^(2)-1).4x^(3))/(x^(8))=(4x^(5)-8x^(5)+4x^(3))/(x^(8))`
`=-(4x^(5)+4x^(3))/(x^(8))= (4x^(3)(-x^(2)+1))/(x^(8))`
Also, `f^(')(x) lt 0`
`rArr (4x^(3)(1-x^(2)))/(x^(8)) lt 0 rArr x^(2) gt 1`
`rArr x gt +-1`
`therefore x in (1,infty)`