Exam 4: Using the Derivative

Find a value of a such that the function has a critical point at .

The following figure is a graph of a derivative function, . Indicate on the graph the x-values that are critical points and label each as a local maximum, a local minimum, or neither.

If the cost function is . For the 120^th unit, find the marginal cost and average cost, identify the units.

The total revenue, R, in dollars,when selling q items is . Calculate and interpret the marginal revenue if q= 10.

Rank the following products from 1 to 4 according to their elasticity, with 1 being the highest. A. high performance automobile B. cellular phone C. laundry detergent D. movie theater tickets

If for , what is ?

Total cost and revenue are approximated by the functions and , both in dollars. A. What is the fixed cost? B. What is the profit function?

Estimate the inflection points of if the following graph is the graph of A. B. C. List inflection points in increasing order of x-coordinates; separate each point with a comma.

Suppose f has a continuous derivative whose values are given in the following table. Is x=-2.5 a potential local minimum, local maximum, or neither?

A disease is released into a small town. The number of people infected is modeled by the equation . What is the population at t=0 of this disease?

The cost function, in dollars, is . The average cost of producing 130 units is .

The elasticity for a good is E=1.3. What is the effect on demand of a 7% price increase?

A factory produces a product that sells for $12. They currently produce 2200 items per month, at an average cost of $3 per item. The marginal cost at this level is $2. Assume that the factory can sell all the items that it produces. A. What is the profit at this production level? B. Would increasing production increase or decrease profit?

The following is a graph of . Which of the following statements about are true?

Does the maximum value of the surge function increase or decrease when a is increased and b is held constant?

On the following graph, the point (4,3.5) is a

The peak concentration of 9 ng/ml for a drug occurs 1.5 hours after a 7 mg dose is administered. Sketch a graph that represents the concentration, C, as a function of time, t.

An amusement park finds that when it charges $15 for an all-day pass, attendance is about 2400 per day. When it charges $19 , attendance is about 2200 per day. Is daily revenue higher at a price of $15 or a price of $19?

The average cost per item to produce q items is given by for q>0. At what point q (to two decimal places) does marginal cost equal average cost?

If time, t, is in hours and concentration, C, is in ng/ml, the drug concentration curve for a drug is given by . Suppose scientists wish to alter the drug so that it is effective for more hours. Would the coefficient of 9 in its concentration curve equation increase or decrease?