\fduring a particular day. (See Example 2.) In Exercises 19 and 20, P(t) is the price of a certain stock at time t 19. Finance If the price of the stock is falling faster and faster, are P'(r) and P*(r) positive or negative? Explain your answer. +.49 +1.876 +2 53% $ 42 4 +45% $1.17 LINCHFind the largest open intervals on which each function is concave upward or concave downward, and find the location of any points of inflection. (See Example 4.)27. [(x) + 4r - 6r + 331. /(x) + 8r - 30r- + 24x - 3Business In Exercises 33-36, find the point of diminishing re- turns for the given functions, where R(x) represents revenue, in thousands of dollars, and x represents the amount spent on adver- tising, in thousands of dollars. (See Example 5.)\fFind all critical numbers of the functions in Exercises 37-48. Then use the second-derivative test on each critical number to determine whether it leads to a local maximum or minimum.37. /(x) 72x + 1\f57. Physical Science When an object is dropped straight down, its position, in feet, after / seconds is given by $(0 = -1612. Note that negative velocity indicates downward motion. Find the velocity at each of the following times. (a) After 3 seconds (b) After 5 seconds (c) After 8 seconds (d) Find the acceleration. (The answer here is a constant, the acceleration due to the influence of gravity alone.)Work these problems. You may need to use the quadratic formula to find some of the critical numbers. (See Example 6.) 61. Finance The U.S. gross domestic product (in billions of dol- lars) can be modeled by /(x) = 192 - 500r + 4536r (45x 5 12), where x = 4 corresponds to the year 2004. Find and interpret the point of inflection. (Data from: www.bea.gov.)