Answer Happy

1. It is estimated that x months from now, the population of a certain community will be P(x) = x2 +20x + 8000. (a) At what rate will the population be changing with respect to 15 months from now?. (b) By how much will the population actually change during the 16th month ?. 2. Find the derivative of y = 22 +22-21 3. A manufacturer estimates that r units of a certain commodity are produced and sold, the revenue derived will be R(x) = 0.5x2 + 3x – 2 thousand dollars. At what rate is the revenue changing with respect to the level of production x when 3 units are being produced? Is the revenue increasing or decreasing at this tiite? 4. Given that the total cost function for a certain commodity C(x) = 5x2 + 3x + 98. (a) Find the average cost and the marginal average cost for the commodity. (b) For what level of production is the marginal avearge cost equal to 0? (c) For what level of production is the marginal avearge cost equal average cost? 5. Suppose the total cost in dollars of manufacturing a units of a certain commodity is C(x) = 3x2 + 5x +10. If the current level of production is 40 units, estimate how the cost will change if 40.5 units are produced. 6. Find the value of the derivative at ()1,3 of y = xr? - xy + 2xy? – 4y? = 0.