OF CHANGE 1. The management of the Titan Tire Company has detemined that the weekly demand function for their Super Titan tires is given by p = f(x)= 144-x where p is the price of tires measured in dollars and x is the demand measured in units of a thousand. A. Find the price when 5000 tires are sold. (x = 5) B. Find the price when 6000 tires are sold. (x = 6) C. Find p(6) - p(5) p(6)- p(5) f(x+ Ar) - f(x) D. Find This is 6-5 Ar This value is the average rate of change of the unit price of a tire, or the marginal rate of change of the price. Following the outline above: (remember, tires are in units of 1000!) Show all of your computational steps. A. Find the average rate of change between 5000 and 5100 tires. B. Find the average rate of change between 5000 and 5010 tires. Interpret your results. Find the instantaneous rate off change per 1000 tires. (This is f'(x)) Interpret the results and compare this with your previous answer. 2. The temperature T of a person during an illness is given by T(1) = -0.11 +1.21 +98.6 Where T is the temperature, in degrees Fahrenheit, at time r in days. A. Find the rate of change of the temperature with respect to time. B. Find the temperature at t=1.5 days. C. Find the rate of change at t=1.5 days: Eaiy All s Resened ० PTongs *4mx114im(24 cm x 29 cm) 12. The view V, or distance, in miles that one can see to the horizon from a height h, in feet, is given by V = 122 h A. Find the rate of change of V with respect to h. B. How far can one see to the horizon from an airplane window from the height of 40,000 ft? C. How far can one see a ship from the top of a 325 fl. light house? 13. A company has a fixed cost of $30,000 and a production cost of $6 for each unit it manufacturers. A unit sells for $10. A. What is the cost function? B. What is the revenue function? C. What is the profit function? D. Compute the profit (loss) corresponding to production levels for the following units of production: a. 6,000 b. 8,000 c. 12,000 14. For the problem above, determine the "break-even" point in production. What is an appropriate "viewing window" to understand the graph of this problem? *Extra credit if vou can explain your rationale for choosing this viewing window - "because it works" does not count as an answer! 15. Epidemiologists in College Station, Texas estimate that t days after the flu begins to spread in the town, the percent of the population infected by the flu is approximated by: p(t) =1 +1 for 0sr. a. Find the average rate of change of p with respect to t over the interval from 1 to 4 days. b. Find and interpret the instantaneous rate of change of p with respect to at -3.