But notice what happens at a maximum point, a place where the graph is at the largest value.
Critical points are the places to look for a maximum or minimum of the function.
There is a new phenomenon for functions of more than one variable, though. All those things can happen for functions of several variables as well, but the point can also be a saddle point, which is not the same as a plateau. It's stable, not just a bare leveling off, but any nearby surface will also have such a saddle point. There is a test to see what kind of critical point it is, essentially the new version of the second derivative test.