Whoever gave you these problems expects you to know that at a maximum, the first derivative goes from + (going upward) to - (going downward) and so must be 0 at the maximum. Similarly, at a minimum, the first derivative goes from - (going downward) to + (going upward) and so must be 0 at the minimum.

You should be able to tell that is never negative so that the sign of is the opposite of the sign of x. You don't really need to know the second derivative.