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Find the values of x for which y=[x(x-2)...

Find the values of x for which `y=[x(x-2)]^2`is an increasing function

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`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)`.
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