FERMAT: ONE VARIABLE WITHOUT CONSTRAINTS 43 · Problem 9.1.1, "Which number is bigger, e or e ?" illus- trates the distinction between the desire "to reach the essence of things" and the wish to crack a puzzle just for the fun of it. 1.5 DISCUSSION AND COMMENTS 1.5.1 All methods of continuous optimization in a nutshell It is possible to sketch all questions and methods of optimization that we want to present, by discussing these for one-variable problems. We will omit precise assumptions and will make use of some notions that will be defined later in a precise way, such as that of a convex function, meaning that each segment with endpoints on the graph of the function lies nowhere below this graph. If, moreover, no points of these segments lie on the graph except the endpoints, then the function is called strictly convex. Base. What makes it all work? It is, in the first place, the method of linear approximation: this consists of the differential calculus and a powerful result, the tangent space theorem. The differential calculus