(i) A maximum point is a point where regardless if you move right or left, the height will decrease.  A visual analogy would be a hill: if you're at the top of a hill, no matter which direction you go your height will decrease.  So you're looking for a part of the graph which is 'like a hill', and in this graph the point is at $(\var{xmax}, \var{ymax})$.

(ii) A minimum point is the opposite of a maximum point (or an upside-down version of a maximum point, if you like).  The analogy in this case would be a valley: no matter which direction you go your height will increase.  In this graph, the minimum point is at $(\var{xmin}, \var{ymin})$.