Page "Maxima and minima" Paragraph 30

In contrast, there are substantial differences between functions of one variable and functions of more than one variable in the identification of global extrema.

For example, if a bounded differentiable function f defined on a closed interval in the real line has a single critical point, which is a local minimum, then it is also a global minimum ( use the intermediate value theorem and Rolle's theorem to prove this by reductio ad absurdum ).

In two and more dimensions, this argument fails, as the function