(Originais Teachy 2023) - Question Easy of Mathematics

A box manufacturer wants to create a new packaging for their products. The shape of the box is defined by a polynomial that represents the volume V(x) of the box as a function of the height x of the square base. The polynomial describing the volume of the box is given by V(x) = x^3 - 6x^2 + 9x. To optimize the use of material, the company wants to determine the height of the base that maximizes the volume of the box. Use Girard's relations to find the sum of the roots of the polynomial V(x). Then, determine the height x that maximizes the volume of the box. (Consider that the value of x is positive and that the unit of measure of the height is the same as the square base, so it does not interfere with the optimization analysis).