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.) The slope of the tangent line to a curve is given by f'(x) = 8x2 + 7x- 2. If the point (0.1) is on the curve, nd an equation of the curve. E) f(x) = D The marginal prot in dollars on Brie cheese sold at a cheese store is given by P'(x) = x(80x2 + 90x) , where x is the amount of cheese sold, in hundreds of pounds. The "prot" is - $70 when no cheese is sold. a. Find the profit function. b. Find the prot from selling 200 pounds of Brie cheese. a. Find the profit function. P(x) = b. Find the prot from selling 200 pounds of Brie cheese. The prot from selling 200 pounds of Brie cheese is $ The marginal revenue (in thousands of dollars) from the sale ofx gadgets is given by the following function. 2 R'(x) = 4x (x2 + 26,000) 3 3. Find the total revenue function if the revenue from 120 gadgets is $45,879. b. How many gadgets must be sold for a revenue of at least $40,000? (3) a. The total revenue function is R(x) = D, given that the revenue from 120 gadgets is $45,879. (Round to the nearest integer as needed.) b. D gadgets must be sold to generate a revenue of at least $40,000. (Type a whole number.) Use the denite integral to nd the area between the xaxis and f(x) over the indicated interval. Check first to see if the graph crosses the xaxis in the given interval. f(x) = 6x 18; [2.6] E> The area between the xaxis and f(x) is E. (Type an integer or a simplied fraction.) Use the definite integral to find the area between the x-axis and f(x) over the indicated interval. Check first to see if the graph crosses the x-axis in the given interval. f(x) = ex - 4; [- 1,4] . . . The area between the x-axis and f(x) is (Do not round until the final answer. Then round to three decimal places as needed.)The rate at which a substance grows is given by R'(x) = 125e.4, where x is the time (in days). What is the total accumulated growth during the first 4.5 days? . . . Set up the definite integral that determines the accumulated growth during the first 4.5 days. Growth = ()ax 0 (Type exact answers in terms of e.) Evaluate the definite integral. Growth = (Do not round until the final answer. Then round to one decimal place as needed.)Find the producers' surplus if the supply function for pork bellies is given by the following. S(q)=q7i2+4q5l2+53 Assume supply and demand are in equilibrium at q = 9. c:) The producers' surplus is $El. (Type an integer or decimal rounded to the nearest hundredth as needed.)