math hw

QUESTION 1

· What is the absolute minimum value of 2x5 + 5x4 - 80x3 + 31 on the interval [-2, 5]?



·	·	· -1761
·	·	· -960
·	·	· -687
·	·	· -594
·	·	· None of These

· 


20 points  

QUESTION 2

· An open-topped rectangular box is to be made by taking an 18-inch by 18-inch sheet

of cardboard and cutting identical squares from each corner and then folding up the
sides.  What is the volume of the largest box that can be created in this manner?


· 


·	·	· 324 in3
·	·	· 432 in3
·	·	· 648 in3
·	·	· 864 in3
·	·	· None of These

· 


20 points  

QUESTION 3

· The average vehicle speed (in miles per hour) at a particular point on a highway on a
Monday morning is given by H(t) = 20t - 40t0.5 + 70 on the interval [0, 4] where t is in
hours and t = 0 corresponds to 6 AM.  At what time does the lowest average vehicle
speed occur?



·	·	· 6 AM
·	·	· 7 AM
·	·	· 8 AM
·	·	· 9 AM
·	·	· None of These

· 


20 points  

QUESTION 4

· Suppose that a homeowner has 380 feet of fencing and she wishes to enclose a 

rectangular area at the back of her house with no fencing needed along the house
(this means that only 3 sides of fencing are needed as the house itself will serve as
the fourth side).  What is the maximum area that she can enclose with the fencing 
that she has available?


· 


·	·	· 9,025 ft2
·	·	· 17,850 ft2
·	·	· 18,050 ft2
·	·	· 21,850 ft2
·	·	· None of These

· 


20 points  

QUESTION 5

· Chris Porter started his own manufacturing business producing water bottles an upon

investigation it was found that the profit from making w insulated water bottles per hour 
can be modeled by the equation P(w) = -0.07w2 + 11.48w - 440.68, where w is the number 
of water bottles produced and P(w) is the profit in dollars.  How many water bottles should
Chris' company produce each hour in order to maximize profit?



· 


·	·	· 30
·	·	· 56
·	·	· 82
·	·	· 108
·	·	· None of These