What is the absolute minimum value of 2x 5 + 5x 4 - 80x 3 + 31 on the interval [

Question

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

-1761

-960

-687

-594

None of These

QUESTION 2

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

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

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

QUESTION 5

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

-1761

-960

-687

-594

None of These

Explanation / Answer

1)-594

2) on differentiating P(w) = -0.07w2 + 11.48w - 440.68 we get:-

P' = -0.14w+11.48

to maximize P'=0

hence w = 11.48/0.14=82

w=82

3) H(t) = 20t - 40t0.5 + 70

on differentiating it we get:-

H'=20-0.5*40t-0.5

then making it 0 we get:-

t = 1

hence TIME =6+1 = 7AM

4) let the sides be x and y then 2x+y = 380

area = x*y

now putting the value of y in area

x*(380-2x)

now for maximizing we differentiate and equate to 0 we get:-

x=380/4 = 95

hence y = 380-2*95 = 190

hence the area = 190*95 = 18,050 ft2

5)

648 in3

648 in3

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