# Give the function: y = 2x^3-15x^2+36x-24

August 30, 2017

Question
1.Give the function: y = 2x^3-15x^2+36x-24
a. Find the coordinates of any stationary points (extreme points) on the curve.
b. Determine whether these are relative maxima or minima.
c. Using this information, sketch the curve.

2. Efficiency specialists determine that t hours after beginning a shift a worker’s efficiency on the job is approximately R(t)= 0.92 + 0.08t – 0.02t^2 percent.
a. what is the effieciency after 3 hours?
b.when is effieciency a maximum?

3. George is evaluating the opportunity to expand his business through part ownership in a dishwasher company. In analyzing the business plan of the company, he learns that the price per dishwasher at which he can sell x dishwashers per week is p=600-3x dollars.
Furthermore, the total cost of producing x dishwashers per week is,
C(x)=400+150x+0.5x^2 dollars.

a. Find the revenue function R(x) =xp
b. Find the profit P(x), obtained form selling x dishwashers per week.
c. Find the marginal revenue and marginal cost function.
d. Find the Production level x, for which the profit is a maximum.
e. What is the relationship between marginal cost and marginal cost and marginal revenue for the production level found in d.
What is the maxima profit?

4. A furniture store expects to sell 640 sofas at a steady rate next year. The manager of the store plans to order these sofas from the manufacturer by placing several orders of the same size, spaced equally throughout the year. The ordering cost for each delivery is \$160.00, and carrying cost, based on the aqverage number in stock amount to \$32 per year per sofa.

a. Let x be the order quantity and r the number of orders placed durning the year. Find the inventory cost in terms of x and r.

b. Find the cost in terms of x only.

c. Find the number of sofas that the manager should order so as to minimize the total inventory cost. What is the minimum inventory cost?

5. Find the x coordinates of all relative extreme points of,
f(x)=2/3x^3-7x^2=24x-72

6. Find the relative extreme points for, f(x)=x^3+6x^2-15x

7. what are the x-intercepts of the graph of y=3x^3+24

8. A manufacturer estimates that the profit from producing x units of commodity is -x^2+40x-100 dollars per week. What is the maximum profit he can realize in one week?

9. A rectangular garden of are 50 square feet is to ve surrounded on three sides by a fence costing \$2 per running foot and on one side by a brick wall costing \$6 per running foot. Let x be the length of the brick wall side. which of the following represents the total cost of the material?

10. A toll road averages 36,000 cars per day when charging \$1 (100 cents) per car. A survey concludes that charging the toll will result in 300 fewer cars for each cent of increase in price. Which of the following represents the revenue that will result from an increase of x cents in the price of the toll?

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