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The final exam questions for a quantitative analysis course, covering topics such as derivatives, true or false questions, finding horizontal and vertical asymptotes, critical points, relative maxima and minima, points of inflection, area calculation, cost and revenue analysis, production function, and partial differentiation.

Typology: Exams

Pre 2010

1 / 9

Download Math 1100-005 Final Exam: Quantitative Analysis and more Exams Quantitative Techniques in PDF only on Docsity! Math 1100-005: Quantitative Analysis Final Exam (April 29, 2008) If you do not follow any of the following rules, you will get partial or zero credit. 1. Write everything clearly. 2. Don’t forget to use equal signs appropriately. 3. Show all the steps to solutions for full credit. Don’t forget your conclusion! Name: 1. (20 points) Find the indicated derivative for each of the following func- tions. (a) Find y′ if y = ( 2x− 1 x2 + x )4 . (b) Find y′′ if y′ = (ln x)(e3x 2−4x). 1 2. (20 points) Answer the following true or false questions. Also support your answer if it is false (i.e. Give a counterexample). (a) The derivative of y = eln x for x > 0 is undefined. (b) The average value of a continuous function y = f(x) over the interval [a, b] is given by 1 b− a ∫ b a f(x)dx. (c) The domain of the function f(x, y) = 1√ x2−y2 is all the pairs of x and y where x 6= y. 2 4. (20 points) Find the area of the region enclosed by the following equations: f(x) = x2 g(x) = √ x. Also sketch the region by indicating the functions and the points of inter- section. 5 5. (20 points) A product can be produced at a total cost of C(x) = 800 + x, where x is the number produced and is limited to at most 150 units. If the total revenue is given by R(x) = 80x − 14x 2, determine the level of production that will maximize the profit. 6 6. (20 points) Suppose that for a particular product, the number of units x produced per month depends on the number of thousand of dollars y invested, with x = 30y + 20y2. At what rate will production increase if $10, 000 is invested and if the investment capital is increasing at a rate of $1000 per month? 7