**The question:**
Locate and identify the stationary points for

**My attempt:**
Using quotient rule...

I find when this equals zero, i.e.

Therefore,

I substitute this into the original eqn to get 1/2 and -1/2. So the points are (1, 1/2) and (-1, -1/2). So far so good.

Now I want to know the nature of these points. So I go to find the second derivative...

Looks a bit messy!

I substitute 1 into the equation and get a negative number, so I gather that (1, 1/2) is a maximum point. However, when I substitute -1, I get 0.