1. AP Calculus BC
September 29, 2016

2. Entry Task
A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimensions will produce a box with maximum volume?
Ratio, dividing by x^2, calculator

3. Learning Targets
I understand how to apply derivatives to solve a variety of problems.
I solved applied optimization problems (determining the maximum or minimum).

4. Optimization Problems
Identify given quantities, quantities to be determined, and make a sketch.
Write a primary equation for the quantity to be maximized or minimized.
Reduce the primary equation into an equation with a single independent variable. A secondary equation relating the variables of the primary equation may be needed.
Determine the feasible domain of the primary equation.
Use calculus to determine the optimum value.

5. Two posts, one 12 feet high and the other 28 feet high, stand 30 feet apart. They are to be stayed by two wires, attached to a single stake, running from ground level to the top of each post. Where should the stake be placed to use the least amount of wire?

6. Assignment #15
§3.7 - Page : 7, 13, 16, 21, 25, 26, 41