Suppose that the cost (in dollars) for a company to produce @ pairs of a new line of jeans is C(x) = 2000 + 3x + .01x2+ .0002x-3. (a) Find the marginal cost function. (b) Find C" (100). (What does this mean?) (c) Find the cost of manufacturing the 101 pair of jeans. (a) C'(x) (b) C' (100) dollars/pair (c) Cost = dollarsThe total cost (in dollars) of producing a coffee machines is C(x) = 2100 + 50x - 1x2. (A) Find the exact cost of producing the 21st machine. Exact cost of 21st machine = (B) Use marginal cost to approximate the cost of producing the 21st machine. Approx. cost of 21st machine =The total profit (in dollars) from the sale of @ answering machines is P(x) = 20x - 0.4x2 - 300. (A) Find the exact profit from the sale of the 26th machine. Exact Profit on 26th machine = (B) Use the marginal profit to approximate the profit from the sale of the 26th machine. Approx. profit on 26th machine =A company decides to begin making and selling memory sticks for computers. The price function is given as follows: 30000 P = x+2' where T is the number of memory sticks that can be sold every week at a price of p dollars per unit. Additionally, the financial department has determined that the weekly fixed cost of production will be 2500 dollars with an additional cost of 22 dollars per unit. (a) Find the revenue function in terms of x. R(x) = (b) Use the financial department's estimates to determine the cost function in terms of . C(x) = (c) Find the profit function in terms of T. P(x) = (d) Find the marginal profit when 40 memory sticks are produced and sold each week. Marginal profit =\fThe figure below shows f (a ) and its local linearization at a = a, y = 2x - 4. (The local linearization is shown in blue.) What is the value of a? a = What is the value of f (a)? f(a) =[ Use the linearization to approximate the value of f (2.6). f (2.6) = Is the approximation an under- or overestimate? (Enter under or over.)\fCurrently, the share price of a stock is decreasing at a rate of 35 cents per hour, and based on the recent past, the rate of change in this rate of change is negative. If the share price when markets opened today was $8, then the share price 2 hours after markets opened would be approximately dollars and this is most likely to ? the true value of the stock. ? overestimate underestimate determine exactly