051Exam3bsoln

051Exam3bsoln - EXAM 3 March 31, 2005 NAME: Make sure to...

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Unformatted text preview: EXAM 3 March 31, 2005 NAME: Make sure to read the question carefully and answer the question that is asked. Show ALL relevant work so that partial credit may be given and indicate where the solution is. Lack of sufficient work may result in a loss of credit, even if a correct answer is given. Although most of the problems are worth 5 points, this does not mean that they are all of equal difficulty. Good luck!! On my honor, as a University of Colorado at Boulder student, I have neither given nor received unautho- rized assistance on this work. YOUR SIGNATURE: 1. Absolute Extrema (5 points) Find the absolute maximum value and the absolute minimum value of the function on the indicated interval. f ( x ) = 2 x 3 + 3 x 2- 12 x + 2 on the interval [0 , 3] Solution To begin, we find the critical points of the function. f ( x ) = 6 x 2 + 6 x- 12 Since f ( x ) is never undefined, we just need to find where 6 x 2 + 6 x- 12 = 0 6( x 2 + x- 2) = 0 6( x- 1)( x + 2) = 0 So, x = 1, and x =- 2, but x =- 2 is not in the domain of of our function. So, there is one critical point and two endpoints that we just need to compare. f (0) = 2(0) 3 + 3(0) 2- 12(0) + 2 = 2 f (1) = 2(1) 3 + 3(1) 2- 12(1) + 2 =- 5 f (3) = 2(3) 3 + 3(3) 2- 12(3) + 2 = 47 So, clearly the maximum value is 47 at x = 3 and the minimum value is- 5 at x = 1. 1 2. Applied Max/Min (5 points) A manufacturer of baseball bats finds that the total cost (in dollars) of manufacturing x bats per day is given by C ( x ) = 40 , 000 + 400 x + 0 . 1 x 2 ....
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This note was uploaded on 05/03/2008 for the course MATH 1081 taught by Professor Johanson during the Spring '08 term at Colorado.

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051Exam3bsoln - EXAM 3 March 31, 2005 NAME: Make sure to...

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