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

Explanation

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


differentiating both sides w.r.t. `x`


`f^'(x)=(x-1)^3 d/(dx)(x-2)^2+(x-2)^2d/(dx)(x-1)^3`

`f^'(x)=(x-1)^3xx2(x-2)+(x-2)^2xx3(x-1)^2`

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

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

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