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UMass Amherst MATH 127 - Math127 Exam2 SP2013 V1

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Math127 Exam 2 April 10th , 2013 Special Code: 041013 Name _____________________________________________________________ Signature __________________________________________________________ Student ID Number (all 8 digits) ____ ____ ____ ____ ____ ____ ____ ____ ______________________________________________________________________________ Please shut off all cell phones, ear phones, computers, beepers, etc… Please put everything away except a #2 pencil and a calculator that is not attached to a cell phone. You will have 90 minutes to complete the twenty-five multiple choice questions on this exam. Each question is worth four points. If you need more paper or have a question during the exam, please raise your hand and we will come to you. It is very important that you fill in your answers (the “bubbles”) on the answer sheet correctly so that the grading machine reads your answers correctly. Please be conscientious in filling out the bubble sheet. 1. Please fill in the information at the top of this page. 2. On the bubble sheet where it says “Name,” please print your last name, leave a space, and then print your first name in the rectangles. Then fill in the bubbles underneath. 3. On the bubble sheet, where it says “Identification Number,” please CAREFULLY write your entire Student ID number in the rectangles and fill in the bubbles underneath. Please double check to make sure you bubbled in your ID # correctly. 4. On the bubble sheet, where it says “Special Code” please write the number 041013 in the rectangles and fill in the bubbles underneath. 5. On the bubble sheet, where it says “Grade” or “Educ” bubble in your section number Calden 9:30 [1] Benincasa 11:15 (2) Benincasa 12:20 (3) Farelli 2:30 [4] 6. Lastly do not write anything in the sections labeled “Sex” or “Birth date” Please double check that you bubbled your answers correctly on the bubble sheet and circle your answers on your test booklet before you hand it in. When you are finished, quietly gather your belongings and come to the front of the room. Have your student ID card ready to show us. Grades will be posted on your MOODLE page just as soon as they are done. Please do not call or email asking for your grade. We cannot give grades out by phone or email. GOOD LUCK!!1) Suppose ( ) and ( ) ( ). If ( ) ( ( )) find ( ). (A) ( ) (B) ( ( )) * ( ) (C) ( ( )) (D) ( ( )) *( ( )) 2) Find the derivative of ( ) . (A) ( ) ( ) (B) ( ) ( ) (C) ( ) ( ) (D) ( ) 3) Which of the following is the derivative of ? (A) ( ) (B) ( ) (C) (D) 4) Find the derivative of ( ) ( ). (A) ( ) ( ) (B) ( ) ( ) (C) ( ) ( ) (D) ( ) ( )5) Which of the following is the second derivative of y ( ) ? (A) ( ) ( ) (B) ( ) ( ) (C) ( ) (D) ( ) 6) The function ( ) has a critical number at . If you determine ( ) is positive, ( ) is negative, and ( ) is negative, which of the following is true? (A) is an inflection point. (B) is a local maximum. (C) is a local maximum. (D) is a global minimum. 7) Given the following table of ( ), which statement is most accurate: x 0 2 4 6 8 10 12 14 f ‘ (x) 8 6 1 -3 -5 -2 -1 2 (A) ( ) has a local maximum between x = 4 and x = 6 and a local minimum between x = 12 and x = 14. (B) ( ) has a local maximum at x=0 and a local minimum at x=8 (C) ( ) has a local maximum between x = 12 and x = 14 and a local minimum between x = 4 and x = 6 (D) ( ) has a local maximum value of 8 and does not have a local minimum. 8) Determine the points of inflection and intervals of concavity for the function ( ) (A) ( ) has inflection points at ( ) is concave down for and and concave up for (B) ( ) has one inflection point at ( ) is concave down for and concave up for . (C) ( ) has no inflection points and is concave down for all . (D) ( ) has inflection points at ( ) is concave down for and concave up for9) Find the inflection point(s) of the function ( ) : (A) ( ) has an inflection point at x=1 (B) ( ) has an inflection point at x=2 (C) ( ) has an inflection point at x=3 (D) ( ) 10) Find the global maximum and global minimum of the function ( ) on the interval . Which of the following is true? (A) The global minimum is 0 and the global maximum is (B) The global minimum is –5 and the global maximum is 0 (C) The global minimum is 0 and the global maximum is ⁄ (D) There is no global minimum or global maximum. 11) Find the global minimum and global maximum values of the function on the interval. ( ) on . (A) Global maximum: ( ) Global minimum: ( ) (B) Global maximum: ( ) Global minimum: ( ) (C) Global maximum: ( ) Global minimum: ( ) (D) Global maximum: ( ) Global minimum: ( ) 12) Suppose the revenue for a company is given by ( ) and cost is given by ( ) . Remembering that profit is revenue minus cost, find the maximum profit this company can achieve. (A) $55 (B) $8,625 (C) $10,270 (D) $15,350 13) If t is in years since 2000, one model for the number of rose bushes sold per year at a local garden center, y, is given by the equation . During which of the following years were rose bushes selling the fastest? (A) 2000 (B) 2001 (C) 2002 (D) 200514) The spread of a virus through a community can be modeled with the logistic equation ( ), where t is time in weeks and ( ) represents the number of people infected with the virus. Suppose that 10 people originally have the virus, and the number of people infected is increasing approximately exponentially, with a continuous growth rate of 1.45. It is estimated that, in the long run, approximately 4600 people will be infected.


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UMass Amherst MATH 127 - Math127 Exam2 SP2013 V1

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