Find the intervals in which `f(x)=(x-1)^3(x-2)^2` is increasing or decreasing.

Explanation

Given `f(x)=(x-1)^3(x-2)^2`

`f'(x)=(x-1)^2. 2(x-2)+(x-2)^2. 3(x-1)^2`

=`f'(x)=(x-1)^2.(x-2)(2x-2+3x-6)`

=`f'(x)=(x-1)^2.(x-2)(5x-8)`

if `f'(x)=0`

Then,it divides into four intervals

`x<1`,`1 < x< 8/5`,` 8/5 < x < 2` and `x>2`

So the function is increasing in `(-oo,1),(1,8/5),(2,oo)`

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