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MATH 111
Exam II - Version 1 February 24, 2005
Name
Student ID #
Section
Total 50
- You are allowed to use a calculator, a ruler, and one sheet of handwritten notes.
- Please check that your exam contains three problems.
- Please turn your cell phone OFF and put it away for the duration of the exam.
- Unless otherwise indicated, you must show your work. The correct answer with no supporting work may result in no credit.
- If you use a guess-and-check method when an algebraic method is available, you may not receive full credit.
- Write your answers in the specified locations.
- If you need more room, use the backs of the pages and indicate to the reader that you have done so. If you still need more paper, please ask for some.
- When rounding is necessary, round your final answer to two digits after the decimal.
- Raise your hand if you have a question.
- Put your name on your sheet of notes and turn it in with the exam.
- You have 50 minutes to complete the exam.
GOOD LUCK!
- (19 points)
The graphs of two functions f (x) and g(x) are given at right. The formula for g(x) is
g(x) = − 3 x^2 + 24x + 10.
The graph of f (x) is a straight line. The graphs of f (x) and g(x) intersect at x = 0 and at x = 5.
10
5
g(x)
f (x)
x
y
6
(a) Compute
g(x + 2) − g(x) 2
. Simplify as much as possible.
ANSWER:
g(x + 2) − g(x) 2
(b) For what value of x is
g(x) − g(0) x
ANSWER: x = (c) Find the linear formula for f (x).
ANSWER: f (x) = (d) Give the largest value of x at which the graph of g(x) is 10 units higher than the graph of f (x).
ANSWER: x =
- (20 points) You sell Items. You charge p = 90 − Kq dollars per Item for an order of q Items. Your average cost per Item to produce an order of q Items is
AC(q) = 0. 01 q^2 − 1. 26 q + 52.92 +
q
dollars.
(a) On an order of 15 Items, the price per item is $78.75. Find the value of K.
ANSWER: K =
(b) Give the longest interval on which total revenue (T R) is increasing.
ANSWER: from q = to q = Items (c) What is the value of your fixed cost?
ANSWER: F C = dollars (d) Compute the variable cost for 10 Items.
ANSWER: dollars (e) Set up the equation that you would solve in order to find all the quantities at which profit is $1000. Put your equation in the form
Aq^3 + Bq^2 + Cq + D = 0, with A > 0.
DO NOT ATTEMPT TO SOLVE THE EQUATION.
ANSWER:
