Very weird question relating to critical points
I've done some work on this, though either I've hit a strange answer or I did something wrong. The question has two parts.
a) What happens to at for ? Classify the critical point at .
Working out the problem, I got to here:
This, however, leads to the answer , which is an inconclusive answer (it's not a maximum, minimum, or saddle point).
Is this the answer that's being asked of, or did I miss a detail?
b) Repeat for .
I haven't gotten to this yet, but it probably won't take too long.