$3.(2$ pts$)$ Suppose we are maximizing some unknown quantity $\backslash ($ f$($x$)\backslash )$ on the domain $\backslash (0\backslash$leq x $\backslash$leq $10\backslash )$ and we find that $\backslash ($ a $\backslash )$ is a critical point of $\backslash ($ f $\backslash ).$ It's possible that $\backslash ($ a $\backslash )$ is the solution to our optimization problem, but it might not be$.$

For what reasons might $\backslash ($ a $\backslash )$ not be the solution? Name $4$ distinct reasons.

If you can name a $\backslash (\backslash$mathbf$\{5\}\backslash )$ th reason, you will get $0\mathrm{.}5$ bonus points.