3. (2 pts) Suppose we are maximizing some unknown quantity $f(x)$ on the domain $0 \leq x \leq 10$ and we find that $a$ is a critical point of $f$. It's possible that $a$ is the solution to our optimization problem, but it might not be.
For what reasons might $a$ not be the solution? Name 4 distinct reasons.
If you can name a 5th reason, you will get 0.5 bonus points.