8. Task Sort We've used a lot of different tools to answer a lot of different questions. In each part, you will be given a problem to start solving. First, determine which tool to use to solve the problem. Second, follow the corresponding instructions given below (Note- you will NOT necessarily solve the problem given. You'll just start answering it.): Linearization: Write the linearization of the relevant function at a point a that is easy to work with. Newton's Method: Determine a function to which you can apply Newton's Method, then write a formula for Xn+ 1 in terms of X. Recall that *n+ 1 = X, - Jan ' (xn ) Graphing (making tables): Determine the critical numbers, then set up a table/chart that you could use to determine where the function is increasing decreasing. You need to provide the intervals, but you do NOT need to fill in the rest of the chart. Optimization: Find a function (in one variable) that can be used to find the extreme value needed. Related Rates: Fully complete the related rates problem. Each approach is used exactly once. a. The derivative of a function is _-5x+6 VA-X ". Draw a potential sketch of the function. b. Approximate the value of e0.1 c. Find the maximum volume of a triangular prism with a surface area of 50 cm and whose base is an equilateral triangle. d. Approximate a solution to the equation 4* + x4 = 4. e. Consider a hemisphere, or a sphere that has been chopped in half. The sphere is growing and shrinking over time. Suppose that after 15 seconds, the radius is 4 and is growing at a rate of 2 in /sec. How fast is the surface area changing? (Don't forget to count the base of the hemisphere in your surface area.)