Question

Is `f(x)=(x-2)^2/(x-1)` increasing or decreasing at `x=2`?

Answer 1

Find the first derivative , then determine if it is positive (increasing) or negative (decreasing) at `x=2`

Explanation:

Using the quotient rule , then simplify ...

`f'=((x-2) x)/(x-1)^2`

Now, `f'(2)=0`

So, at `x=2`, the derivative equals zero which indicates a critical point that is neither increasing or decreasing .

Hope that helped