Find the values of `x` for which `f(x)=[x(x-2)]^2` is an increasing function. Also, find the points on the curve, where the tangent is parallel to x-axis.

Explanation

`y = [x-2)]^(2)`
` rArr(dy)/(dx) = 2x(x-2)*d/(dx) [x(x-2)]`
` = 2x(x-2)(2x-2)= 4x(x-1)(x-2)`

Let `(dy)/(dx) = 0`
`rArr 4x(x-1) (x-2) = 0`
`rArr x=0 or x=1 or x=2`

`:. y" is increasing function in "(0, 1) cup (2, infty)`.