Assignment 7 Solutions

# Assignment 7 Solutions - MGSC 1206.2 Assignment#7 Winter...

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MGSC 1206.2 Assignment #7 Winter 2008 TOTAL POINTS = 50 Note: Points will be deducted if you do not (a) show your work including suitable calculations, (b) use proper notation, and (c) answer word problems with words. Hand in your answers to the following four questions: 1. For the function g(r) = r 3 – 3r 2 – 24r + 5 answer the following (assuming for now that the variable r can take any value): a) Determine where the function is concave upward and where it is concave downward. g’(r) = 3r 2 – 6r – 24 g”(r) = 6r – 6 > 0 if and only if r>1 So g is concave upward if g”(r)>0 i.e. for all r>1 and g is concave downward for all r<1 b) Find the critical numbers for the function, i.e. where its derivative equals zero. g’(r) = 3r 2 – 6r – 24 = 0 for critical numbers. Use quadratic formula, or factor: g’(r) = 3r 2 – 6r – 24 = 3(r 2 – 2r – 8) = 3(r+2)(r-4) = 0 so r = -2 or r = 4. c) Use the results of (b) and the Second Derivative Test to determine where the function has a relative maximum and/or a relative minimum. The critical numbers are r = -2 or r = 4. Use the Second Derivative Test by checking whether g”(r) = 6r – 6 is positive or negative. g”(-2) = 6(-2) – 6 = -12 – 6 = -18 < 0 so r=-2 is a relative maximum g”(4) = 6(4) – 6 = 24 – 6 = 18 > 0 so r=4 is a relative minimum d) If in fact it is only feasible for the variable “r” to be in the range 0 ≤ r ≤ 6, find the absolute maximum and absolute minimum of the function g(r) in its feasible range. So the absolute maximum is 5 (at x=0) and the absolute minimum is -75 (at x=4). r g(r) 0 5 4 -75 6 -31 3 pts 3 pts 3 pts 3 pts 3 pts

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2. A company is seeking productivity improvement using a training program to improve the skills of its staff. It has been found that if all staff take t hours of instruction in the program, this produces increased revenues for the company in the amount of R t t t ( ) = - 15 2 1 3 3 . a)
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## This note was uploaded on 10/25/2011 for the course MATH 1216 taught by Professor Jang during the Spring '11 term at Saint Mary's University Texas.

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Assignment 7 Solutions - MGSC 1206.2 Assignment#7 Winter...

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