1.Constructing Rain Gutters. A rain gutter is to be made of aluminum sheets that are 20 inches wide by turning up the edges 90 degree. what depth will provide maximum cross sectional area and hence allow the most water to flow?

2. Maximizing the Volume of a Box. A box with a rectangular base is to be constructed such that the perimeter of the base of the box is to be 40 inches. The height of the box must be 15 inches. find the dimensions of the box such that the volume is maximized. what is the maximum volume?

3. the Graphing calculator. the left side of rectangle is -7, right side 5, upper 10, lower -20. the vertex is (-1, -16). in that screen, graph the family of parabolas f(x) =x^2 + bx + 1 for b = -4, b= 0, and b= 4. describe the role of that b plays in the graph for this family of functions.