For a certain product, cost C and revenue R are given as follows, where x is the number of units sold in hundreds. Revenue: 898(x - 5)2 + 22R2 = 13,750 dC a. Find the marginal cost a at x=5. The marginal cost is estimated to be $|:|. (Do not round until the nal answer. Then round to the nearest hundredth as needed.) dR b. Find the marginal revenue 5 at x = 5. The marginal revenue is estimated to be $|:|. (Do not round until the nal answer. Then round to the nearest hundredth as needed.) Use the Fundamental Theorem to show that the following is true. C f ( * ) dx = f ( * ) dx + f ( * ) dx a a C . . . Use the Fundamental Theorem of Calculus to rewrite the left side of the equation. f ( x ) dx = aA small company of science writers found that its rate of prot (in thousands of dollars) after t years of operation is given by the function below. 1 3 P'(t) = (3t+ 3) (t2 + 2t + 2) a. Find the total profit in the rst three years. b. Find the profit in the fourth year of operation. (2. What is happening to the annual prot over the long run? <:> a. The profit in the rst three years is $D. (Round to the nearest dollar as needed.) Find the area between the curves. x=0, x=4, y=2e3x, y=33x+e9 The area between the curves is approximately |:|. (Round to the nearest whole number as needed.) Use a graphing calculator to find where the curves intersect and to nd the area between the curves. y=e , y= -4x2 -6x a. The left point of intersection is El. (Type integers or decimals rounded to the nearest thousandth as needed. Type an ordered pair.) A construction company has an expenditure rate of E'(x) = 20'1 1" dollars per day on a particular paving job and an income rate of |'(x)= 115.6 eo'HX dollars per day on the same job, where x is the number of days from the start of the job. The company's profit on thatjob will equal total income less total expenditures. Prot will be maximized if the job ends at the optimum time, which is the point where the two curves meet. (a) Find the optimum number of days for the job to last. (b) Find the total income for the optimum number of days. (0) Find the total expenditures for the optimum number of days. (d) Find the maximum profit for the job. (a) days (Round to the nearest integer as needed.) Suppose that all the people in a country are ranked according to their incomes, starting at the bottom. Let x represent the fraction of the community making the lowest income (0 5x 5 1); x = 0.4, therefore, represents the lower 40% of all income producers. Let |(x) represent the proportion of the total income earned by the lowest x of all people. Thus, |(0.4) represents the fraction of total income earned by the lowest 40% of the population. The curve described by this function is known as a Lorenz curve. Suppose |(x) = 0.91x2 + 0.09x. Complete parts a through e below. E) a. Find and interpret |(0.2). |(0.2) = (Round to three decimal places as needed.)