Exam 4: Using the Derivative

Sketch a graph of a function such that at x = -1, > 0 when x< -1, > 0 when x > -1.

The cost of producing q items is dollars. What is the average cost of producing the 20^th item?

For and , which of the following statements are true?

Find all of the critical points of . List them from smallest to largest, separated by commas.

If the total revenue and total cost (in dollars) are given by ? What quantity of gadgets, to the nearest whole number should be produced to maximize profit? What is the maximum profit?

Given the curve , with , find the relation between the parameters a, b, and c that will ensure that the curve has no turning points.

If time, t, is in hours and concentration, C, is in ng/ml, the drug concentration curve for a drug is given by . What is the peak concentration of the drug?

The demand equation for a product is , where q is the number of units produced, p is the price of each unit, and a and b are positive constants. Find a formula, in terms of p, for the elasticity of demand.

With x people aboard, a South African airline makes a profit of (1200-4x) rands per person for a specific flight. What is the maximum number of passengers that can board such that the airline still profits?

Given . Which of the following are inflection points of f?

The following table shows the total sales, in thousands, since a new DVD was released. A. Estimate the point of diminishing returns. B. Using your answer from part (A), predict the total possible sales for the DVD.

The graph of a cost function is given in the following figure. Estimate the value of q at which average cost is minimized.

The following table gives the concentration C, of a drug in ng/ml, at time t, in hours, after it is administered to 2 different people. A. If the concentration for Person A is given by and the concentration for Person B is given by , would you expect b_A to be larger or smaller than b_B? B. If the minimum effective concentration is 5 ng/ml, until what time is the drug effective for person A? C. If the minimum effective concentration is 5 ng/ml, until what time is the drug effective for person B?

The average cost per item to produce q items is given by . A. What is the total cost, , of producing q items? B. What is the marginal cost, MC, of producing q items? C. At what production level does marginal cost equal average cost?