M119 Additional Chapter 3 Review

1. For a certain polynomial function

a) Find the first order critical numbers and classify them as a relative

maximum, a relative minimum or neither.

b) Find the second order critical numbers and classify them as inflection

points or neither.

2. The total cost of producing x units of a certain commodity is

a) Find the average cost function, .

b) Determine the minimum average cost of the commodity.

3. If the total cost of manufacturing a commodity is dollars

when x units are produced, and the price per unit function is ,

a) Find the profit function

b) Determine the level of production where the profit is maximized.

c) What is the maximum profit?

d) What price should be charged to produce the largest profit?

4. An industrial psychologist has conducted a study at an appliance factory that

indicates the average worker who arrives on the job at 8 a.m. will have

assembled blenders t hours later, for .

a) At what time is the average worker assembling blenders at the

greatest rate?

b) What is the greatest rate?

5. A citrus grower estimates that if 60 lemon trees are planted in a grove, the

average yield per tree will be 475 lemons. The average yield will decrease by

5 lemons per tree for each additional tree planted in the grove. How many

trees should the grower plant to maximize the total yield?

(Make sure the answer is a whole number)

Solutions

1. a) relative min at x = -1; b) inflection points at x = -4 and x = -2.

2. a) ; b) $1.75 per unit at x = 5/2 or 2.5

3. a) ; b) 20 units;

c) max profit $250; d) price per unit $29

4. a) at 10 a.m; b) 25 blenders/hour 5. 77 or 78 trees