Decide if each of the following problems is a linearization problem, an optimization prob- lem, a related rates problem, a graphing problem, or a Newton's method problem. Identify. Label the problem as one of the five types or explain that it is not exactly one of those types (and how you know). Begin solution. For each problem, start the solution. Linearization. State what function you would linearize and where you would linearize it. Optimization. Draw a diagram to define your variables. Write the function you would optimize, including the domain of the function. Related Rates. Draw a diagram to define your variables. Write an equation that relates your variables. Graphing. State the function, its domain, and any critical points in the domain. Newton's method. State the furlction to which you would apply Newton's method, your initial point, and the Newton iteration. Other. Explain how you might use calculus to solve this problem. where. Poi is planning to build a swimmmg pool. Here are some of his requirements: the surface of the pool should be 1800 ft. Along two opposite sides, he wants the deck to be 5 ft wide, and on the other two opposites sides, he wants the deck to be 10 ft wide. What is the smallest piece of property on which he can place his pool