Page of 10 - ZOOM + Write detailed work to the get full points 1. For the curve given implicitly by y + 3 = 2ry, find the equation of tangent line at (1, 1). [3] 2. Water flows into a cylindrical container at a rate of 6 in /s. Assume that the container has a height of 9 in. and a base radius of 3 in. At what rate is the water level rising in the container? (2]> 0110 O N 3. A rectangular box with a squm bottom and Closed top is to he made from two ma. terials' The material for the side costs $2.00 per square foot and the material far the tap and bottom costs $4.00 per square foot. If you are willing to spend $24 on the box, what is the largest Volume it can contain? Justify your answer completely using calcium. [3] Page of 10 - ZOOM + 4. All units in a 50-unit apartment building are rented out when the rent is set at r = $1500 per month. A survey reveals that for each $50 increase in rent, demand for apartments will decrease, such that one additional apartment becomes vacant. Suppose that each occupied unit costs $100 per month in maintenance. a. Define variables to maximize monthly profit. Write occupied units as a function of rent. b. Determine profit function as a function of single variable. What is the domain on which you should consider this function? [1)