BACHILOR OF SCIENCE DEGREE

IN HUMAN RESOURCE MANAGEMENT

ALTERNATIVE PAPER

MODULE : Calculus 1

DURATION : 2:00 Hours

LECTURER :

INSTRUCTIONS:

1. Please read all instructions carefully before attempting any question.

1. This paper consists of three (3) printed pages and three (3) questions

1. Candidates are required to answer ALL questions 1. PLEASE ENSURE THAT YOU NUMBER YOUR QUESTION CORRECTLY.1. CLEARLY WRITE THE NUMBER OF THE QUESTION ON EACH OF THE RELEVANT PAGES.1. WHERE QUESTIONS HAVE MULTIPLE PARTS, ALL PARTS MUST BE ANSWERED.

Write your IDENTIFICATION NUMBER clearly on each page.

YOUR NAMES SHOULD NOT BE WRITTEN ON THE PAPER, this will result in your script not being marked

DO NOT TURN OVER UNTIL YOU ARE TOLD TO DO SO

1.A car parts manufacturer, situated in the industrial area of the city of Kingston, finds that the total cost of producing and selling x motor vehicle parts, is given by:

Where C(x) is the cost in dollars, and x is the number of car parts manufactured and sold.The companys demand function was also determined to be:

i) As a student excelling in the area of Marginal Analysis, assist the manufacturer in determining the following:a) The domain of the function defined by the price demand function givenb) The marginal cost function C(x)c) The revenue function, and find its domaind) The marginal revenue at x = 100, and interpret the resulte) The profit function and its domainf) The marginal profit when x = 50 and interpret the results[1+2+2+3+3+2]ii) Derive the equation of the function h(z), and determine the value of the arbitrary constant c, given that and h(-1) = 8[3]2.i) Given below is a sketch of the graph of the functions f(x) = 4 + x x2 and g(x) = 1 - x. By applying the correct principle, derive the appropriate integrand and the points of intersection of the curves; hence find the area bounded by the two curves at the points of intersection (that is, the shaded area).

[3+5]ii) The Managing Director of Desnoes and Geddes Bottling Company Limited, having engaged the services of an accounting firm, has been advised that the marginal cost function of his company is as given below:If at zero output, the cost is twenty five dollars ($30)a) Determine the output at which cost is minimizedb) Find the average cost function and the average marginal cost function[3+2+3]3.i) Find the indefinite integrals of the following functions:

[1+2+2+2+3+3]ii) Suppose that a certain function is given by y = 4x x2, find the area that it subtends with the lines x = 0 and x = 2, as shown below

[3]1