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Math 1320 Winter Semester 2006
Exam 2
March 22, 2006
Name: __________________________ Student Number: _________________
Section Number/Instructor Name: _________/_____________________________
Signature:____________________________________
Instructions: This exam consists of both multiple choice and short answer problems. You must show your work for all problems, including the multiple choice problems, to receive credit on them. For the multiple choice problems, you may use a calculator and a pen or pencil, but you may not use any notes or books. Students who cheat will receive zero points on the exam and will be subject to the unversity's disciplinary procedure for academic dishonesty. Cheating includes, but is not limited to, looking at any other student's exam, looking at any books or notes during the exam, or using any electronic device for any purpose other than doing arithmetic. For example, you may not use cell phones, calculators, or any other electronic device during this exam to graph equations or obtain mathematical formulas.
Problem Total Value Student Score
Total 100
- (^) Find an x so that e 2 x^2 −x^ =e^8 −x
A) 1 B) -3 C) -1 D) 2 E) None of these
- (^) True or false: The range of e−^2 x−^1 includes the number -1.
A) True B) False
- (^) Identify the open intervals where the function f ( )x = – x 2 + x+ 4is increasing or
decreasing.
A) Increasing:
; Decreasing:
B)
Decreasing:
; Increasing:
C) (^) Increasing on (^) ( −∞ ∞, ) D) (^) Decreasing on (^) ( −∞ ∞, ) E) None of the above
- The graph of a function f is is shown below:
Which of the following graphs is the graph of its derivative f ′^? (Hint: Use the properties of derivatives to eliminate choices.)
A)
B)
7. Consider the function f ( )x = 6 ( 3 x ) e 2 x+^1. Using calculus, determine which of the
following statements are true.
A) The point x = 0 is not a critical point of f. B) The point x = 0 is a critical point of f, but is not a local extreme point. C) The point x = 0 is a critical point of f, and is a local maximum. D) The point x = 0 is a critical point of f, and is a local minimum. E) None of these are true.
- (^) Find the equation of the tangent line to f ( )x = e−^2 x^ +x^2 at the point x = 2.
A) y − 2 = 2( x− 1) D) y − 1 = 2( x−2) B) y − 1 = −2( x− 2) E) None of these. C) y + 1 = 2( x+2)
Suppose that ( ) 2 4
d f x x dx
= − +. Draw a possible graph for f. On this graph include on
the x-axis the correct x-coordinates of any critical points and any inflection points of f. To recieve credit for your graph, it must be clear from your solution how you used calculus to obtain the graph.
- Depth^ A conical tank (with vertex down) is 10 ft across the top and 18 ft deep. If water is flowing into the tank at a rate of 11 cubic ft per minute, find the rate of change of depth of water when the water is 4 ft deep.
The answers below are correct to two decimal places.
A) 35.64 ft per minute D) 8.91 ft per minute B) (^) 11.34 ft per minute E) None of the above C) 2.84 ft per minute
- A rectangular page is to contain 49 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.
A) 9, 9 B) 7, 7 C) 5, 5 D) 8, 8 E) 6, 6
