Find the intervals where the following functions are (a) increasing and (b) decreasing. `y = (x - 1)^2 (x+2)`

Explanation

`y = 4x^2 + 1/x`
`dy/dx = 8x - 1/x^2`
The function is increasing if `dy/dx gt 0`.
`rArr 8x - 1/x^2 gt 0 rArr x^3 gt 1/8 rArr x gt 1/2`
`therefore` The function is increasing in (1/2, infty)` and decreasing in `(- infty , 1/2).