Introduction

Optimization problems arise in different domains. This chapter introduces some applications and explores how to model a situation as an optimization problem. The points where an optimal quantity is attained are looked for in subsets that can be one dimensional, multi-dimensional, open, closed, bounded or unbounded, etc. With the aid of monotony, and convexity, sketching the graph of a real function is performed by plotting few points. The chapter presents some examples that illustrates how to proceed to graph some surfaces and level curve. It discusses the concept of differentiability to functions of several variables. More precisely, the chapter shows that the existence of a line tangent for a real differentiable function f at a point x₀ is extended to the existence of an hyperplane for a differentiable function with several variables. Each partial derivative is also a function of n variables. These functions may themselves have partial derivatives, called second order derivatives.