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5. A mug manufacturer finds that when they price their mugs at $12 they sell 200 mugs. They determine that for each $1 price increase, they will sell 5 fewer mugs per month. What price should they charge to maximize revenue? Justify your solution is optimal.

4. Calculate each integral. You do not need to simplify your answer. Show all work. (a)

(d) The improper integral

3. For the following problems you do not need to simplify your final answers. (a) Find when

(c) Sales of a product are modeled by a function that gives the number of units sold days after the start of the month. If on the 10th day of the month sales are dropping (going down) increasingly rapidly, what can we say about the first and second derivatives of the function ?

Short Answer: You should submit your answers with the multiple choice on Canvas below. If you have additional work you would like to show you may submit it alongside your work on the free response questions on Gradescope.