This chapter explains an exploration of various simple analytical and numerical techniques and MATLAB commands useful for finding the zeros and the extreme of functions of one and two variables. It explores different techniques for finding the real roots of an arbitrary function of one variable. The chapter discusses the graphical method, the numerical techniques known as the Direct Iterative and the Newton–Raphson methods, and the built-in fzero function of MATLAB. It describes some techniques for finding the zeros of a function in one variable, namely the Direct Iterative and the Newton–Raphson techniques. The chapter also explores other techniques for solving the problem when the simple method is not practical. Analytically, searching for the local extreme of a function of several variables consist of solving the simultaneous equations obtained by setting all partial derivatives of the function equal to zeros.