How do I determine if a stationary point on a curve is the maximum or minimum?

If you are comfortable with differentiation. You can take the second derviatve of the equation of the cruve and plug in the x value of the curve. Based on this answer you can determine if it's a maximum, minimum or stationary. A maximum would have a negative value, a minimum a positive and stationary 0. If however you are not comfortable with this method and cannot memorize the different cases you can always substitute a point slightly before and after the point you're interested in. For example if you're considering x =3. You can subsitute 2.5 and 3.5 into your derivative and based on the signs draw a diagram representing the shape of the curve.