An open container (no top) is to be made from a square piece of sheet metal, 20.0 cm on a side, by cutting equal squares from the corners and bending up the sides. Find the side of each cut-out square such that the volume is a maximum (see Exercise 69).

Data from Exercises 69

The entrance to a garden area is a parabolic portal that can be described by y = 4 − x² (in m). Find the largest area of a rectangular gate that can be installed by graphing the function for area and finding its maximum. This is similar to finding the maximum point of a parabola as in Section 7.4.