3. (+ c.r.) Consider the function /(x) = with first and second derivatives f(x) = 273 -24r and (+ + 4] (a) (2 points) Determine all vertical and horizontal asymptotes. (b) (3 points) Determine the intervals on which the function is increasing and de- creasing. Classify all critical and singular points as either local minimums or maximums. (e) (3 points) Determine the intervals on which the function is concave up or down, and any inflection points. (d) (1 point) Sketch the graph of /(s). 4. (5 points + c.r.) Dwight is looking to expand his beet business and sell beet peelers at the local farmer's market. Unfortunately, there is limited demand for such a product, and Dwight estimates his revenue for a beet peelers is determined by the function R(x) = r(80 - 2) dollars per week. Dwight has a fixed cost of paying his cousin Mose of $1000 per week, and a variable cost of 10x dollars per week dependent on the num- ber of beet peelers made. How many beet peelers should Dwight make per week to maximize his profits? Helpful Ideas: . A profit function is determined by taking the revenue earned minus the costs. . A cost function can be determined by adding the fixed and variable costs together. 5. (4 points + c.r.) Without multiplying by the conjugate, determine the value of a such that lim /4+x- V4 - 40 6. (4 points + c.r.) If an initial amount As of money is invested at an interest rate of r compounded n times a year, the value of the investment after t years is A(!) = A. (1 + ! ) - If we let n + co, we refer to this as continuous compounding of interest. Use l'Hopital's to that if interest is compounded continuously, the the amount after t years is A(!) = Avert .1. (+ c.r.) Consider the implicitly defined curve, r' = 16(x* +y') called the Kampyle of Eudorus. (a) (1 point) Determine the z-intercept(s) of this curve. (b) (2 points) For any point on the curve, determine the slope of the tangent line. (c) (2 points) What is the equation of the tangent line that lies in the first quadrant when = = 57 2. (3 points + c.r.) Suppose that the price-demand for a product can be described using p = 0.05r- 0.2r2 + 0.5 where r(p) is the daily demand (in thousands) and p is the unit price (in $). Determine the rate of change in demand when price is $1.50 per unit and interpret the result. dar Note: You are determining ap when p = 1.50