Math 112 - Spring 2007 Exam 2 - Prof. Jennifer Taggart, Exams of Mathematics

This is a math 112 exam from spring 2007, consisting of 12 questions covering derivatives, partial derivatives, tangent lines, local maxima/minima, total cost, average cost, and linear programming. Calculator and one page of notes are allowed.

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Pre 2010

Uploaded on 03/10/2009

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Math 112 - Spring 2007
Exam 2
May 15, 2007
Name:
Section:
Student ID Number:
1 12
2 12
3 14
4 12
Total 50
You are allowed to use a calculator and one hand-written 8.5 by 11 inch page of notes. Put
your name on your sheet of notes and turn it in with the exam.
Check that your exam contains all the problems listed above.
You must show your work on all problems. The correct answer with no supporting work
may result in no credit. Unless otherwise indicated, your final answer must be correct to two
digits after the decimal.
If you use a guess-and-check, or calculator, method when an algebraic method is available,
you may not receive full credit.
If you need more room, use the backs of the pages and indicate to the grader that you have
done so.
Raise your hand if you have a question.
There are multiple versions of the exam. Any student found engaging in academic miscon-
duct will receive a score of 0 on this exam. In addition, students found engaging in academic
misconduct are typically put on academic probation. So DONT CHEAT! It could serious hurt
your career.
You have 50 minutes to complete the exam.
GOOD LUCK!
pf3
pf4
pf5

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Math 112 - Spring 2007

Exam 2

May 15, 2007

Name:

Section:

Student ID Number:

Total 50

  • You are allowed to use a calculator and one hand-written 8.5 by 11 inch page of notes. Put your name on your sheet of notes and turn it in with the exam.
  • Check that your exam contains all the problems listed above.
  • You must show your work on all problems. The correct answer with no supporting work may result in no credit. Unless otherwise indicated, your final answer must be correct to two digits after the decimal.
  • If you use a guess-and-check, or calculator, method when an algebraic method is available, you may not receive full credit.
  • If you need more room, use the backs of the pages and indicate to the grader that you have done so.
  • Raise your hand if you have a question.
  • There are multiple versions of the exam. Any student found engaging in academic miscon- duct will receive a score of 0 on this exam. In addition, students found engaging in academic misconduct are typically put on academic probation. So DONT CHEAT! It could serious hurt your career.
  • You have 50 minutes to complete the exam.

GOOD LUCK!

  1. (12 pts) Compute the indicated derivatives and put a box around your final answer. Do not simplify.

(a) (4 pts) G(w, b) = b^3 m + 4 ln(m) −

b^2

− m^3 b^6 + 7m + 14

∂G

∂b

∂G

∂m

(b) (4 pts) y = ln

( e^3 x^5 +

3 x − 2

)

dy dx

(c) (4 pts) F (x) =

(x^2 + 1)^12 1 + ln(2x + 1)

F ′(x) =

  1. (14 pts) Your Total Cost (in dollars) vs. the quantity q of Items sold is given by the function:

T C(q) =

q^3 3

− 5 q^2 + 21q +

The Average Cost is given by AC(q) =

T C(q) q

(a) (6 pts) Find the two values of x at which the Total Cost graph has a horizontal tangent. Use the Second Derivative Test to determine whether T C(q) reaches a local maximum or a local minimum at each value.

ANSWER: q = gives a local of T C(q);

q = gives a local of T C(q). (b) (4 pts) Give the global maximum and global minimum values of Total Cost on the inter- val from q = 0 to q = 5.

ANSWER: MAX = dollars; MIN = dollars. (c) (4 pts) Is the Average Cost graph concave up, concave down, or neither at q = 3? Justify your answer. Guessing the answer with no supporting work receives zero pts.

ANSWER (circle one): CONCAVE UP CONCAVE DOWN NEITHER

  1. (12 pts) The constraints for a linear programming problem are

4 x + 6y ≤ 1800 , x ≤ 300 , and y ≤ 150.

(a) (4 pts) Sketch the feasible region.

(b) (4 pts) Find the exact coordinates of the vertices of the feasible region. Label all of them on your graph.

(c) (4 pts) Subject to the given constraints, find the maximum value of the objective function: f(x, y) = 14x + 20y.

ANSWER: maximum =