Calculus Quiz

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QUESTION 1

· Solve the problem. Maximize Q = xy2, where x and y are positive numbers, such that x + y2 = 10.

		x = 5, y = $C:\Users\john.morris\Desktop\f1q7g2.jpg$
		x = 0, y = $C:\Users\john.morris\Desktop\f1q7g1.jpg$
		x = $C:\Users\john.morris\Desktop\f1q7g2.jpg$ , y = 5
		x = 1, y = 3

4 points

QUESTION 2

· Solve the problem. From a thin piece of cardboard 10 in. by 10 in., square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary.

		5 in. by 5 in. by 2.5 in.; 62.5 in.3
		6.7 in. by 6.7 in. by 3.3 in.; 148.1 in.3
		6.7 in. by 6.7 in. by 1.7 in.; 74.1 in.3
		3.3 in. by 3.3 in. by 3.3 in.; 37 in.3

4 points

QUESTION 3

· Find the extreme values of the function and where they occur. y = (x - 4)2/3

		The minimum value is 0 at x = 4.
		There are no definable extrema.
		The minimum value is 0 at x = -4.
		The maximum value is 0 at x = -4.

4 points

QUESTION 4

· Find the absolute extreme values of the function on the interval. F(x) = $C:\Users\john.morris\Desktop\f1q20g1.jpg$ , -2 ≤ x ≤ 8

		absolute maximum is 0 at x = 0; absolute minimum is 2 at x = 8
		absolute maximum is 2 at x = -8; absolute minimum is 0 at x =0
		absolute maximum is 2 at x = 8; absolute minimum is 0 at x =0
		absolute maximum is 2 at x = 8; absolute minimum is -2 at x = -8

4 points

QUESTION 5

· Determine all critical points for the function. f(x) = (x - 10)5

		x = 0, x = 10, and x = 5
		x = 10
		x = 10 and x = 5
		x = 0 and x = 10

4 points

QUESTION 6

· Find the absolute extreme values of the function on the interval. f(x) = 3x2/3, -27 ≤ x ≤ 1

		absolute maximum is 27 at x = -27 ; absolute minimum is 3 at x = 1
		absolute maximum is 9 at x = -27 ; absolute minimum is 0 at x = 0
		absolute maximum is 27 at x = -27 ; absolute minimum is 0 at x = 0
		absolute maximum is 3 at x = 1 ; absolute minimum is 0 at x = 0

4 points

QUESTION 7

· Find the absolute extreme values of the function on the interval. f(x) = tan x, - $C:\Users\john.morris\Desktop\f1q23g1.jpg$ ≤ x ≤ $C:\Users\john.morris\Desktop\f1q23g1.jpg$

		absolute maximum is 1 at x = $C:\Users\john.morris\Desktop\f1q23g7.jpg$ ; absolute minimum is -1 at x = - $C:\Users\john.morris\Desktop\f1q23g8.jpg$
		absolute maximum is 1 at x = $C:\Users\john.morris\Desktop\f1q23g1.jpg$ ; absolute minimum is -1 at x = - $C:\Users\john.morris\Desktop\f1q23g1.jpg$
		absolute maximum is -1 at x = $C:\Users\john.morris\Desktop\f1q23g1.jpg$ ; absolute minimum is 1 at x = - $C:\Users\john.morris\Desktop\f1q23g1.jpg$
		absolute maximum is 1 at x = $C:\Users\john.morris\Desktop\f1q23g1.jpg$ and - $C:\Users\john.morris\Desktop\f1q23g1.jpg$ ; absolute minimum does not exist

4 points

QUESTION 8

· Find the extreme values of the function and where they occur. y = x3 - 3x2 + 4x - 4

		The maximum is 0 at x = 2.
		None
		The maximum is 0 at x = 1.
		The minimum is 0 at x = -1.

4 points

QUESTION 9

· Find the absolute extreme values of the function on the interval. f(x) = x4/3, -1 ≤ x ≤ 8

		absolute maximum is 16 at x = 8; absolute minimum is 0 at x = 01
		absolute maximum is 64 at x = 8; absolute minimum is 0 at x = 01
		absolute maximum is 16 at x = 8; absolute minimum does not exist
		absolute maximum is 16 at x = 8; absolute minimum is 1 at x = -1

4 points

QUESTION 10

· Find the extreme values of the function and where they occur. y = $C:\Users\john.morris\Desktop\f1q11g1.jpg$

		The minimum is 6 at x = 0.
		The maximum is 6 at x = -2.
		The minimum is 0 at x = 1.
		The maximum is 6 at x = 2.

4 points

QUESTION 11

· Find the extreme values of the function and where they occur. y = $C:\Users\john.morris\Desktop\f1q25g1.jpg$

		The maximum value is 1 at x = 0.5, the minimum value is -1 at x = 0.5.
		The maximum value is 1 at x = 0.5.
		The minimum value is -1 at x = 0.5.
		The maximum value is 1 at x = 0.

4 points

QUESTION 12

· Solve the problem. A hotel has 280 units. All rooms are occupied when the hotel charges $100 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant. Each occupied room costs $24 per day to service and maintain. What should the hotel charge per day in order to maximize daily profit?

		$102
		$190
		$202
		$192

4 points

QUESTION 13

· Find the extreme values of the function and where they occur. y = $C:\Users\john.morris\Desktop\f1q12g1.jpg$

		The maximum is - $C:\Users\john.morris\Desktop\f1q12g3.jpg$ at x = 0; the minimum is 1 at x = -2.
		The maximum is 3 at x = 0; the minimum is $C:\Users\john.morris\Desktop\f1q12g3.jpg$ at x = -2.
		The maximum is $C:\Users\john.morris\Desktop\f1q12g3.jpg$ at x = 0; the minimum is - 1 at x = -2.
		None

4 points

QUESTION 14

· Find the absolute extreme values of the function on the interval. F(x) = - $C:\Users\john.morris\Desktop\f1q19g1.jpg$ , 0.5 ≤ x ≤ 4

		absolute maximum is $C:\Users\john.morris\Desktop\f1q19g8.jpg$ at x = $C:\Users\john.morris\Desktop\f1q19g9.jpg$ ; absolute minimum is -4 at x =4
		absolute maximum is - $C:\Users\john.morris\Desktop\f1q19g8.jpg$ at x = 4; absolute minimum is -4 at x = - $C:\Users\john.morris\Desktop\f1q19g9.jpg$
		absolute maximum is - $C:\Users\john.morris\Desktop\f1q19g8.jpg$ at x = 4; absolute minimum is -4 at x = $C:\Users\john.morris\Desktop\f1q19g9.jpg$
		absolute maximum is - $C:\Users\john.morris\Desktop\f1q19g8.jpg$ at x = $C:\Users\john.morris\Desktop\f1q19g9.jpg$ ; absolute minimum is -4 at x = -4

4 points

QUESTION 15

· Find the extreme values of the function and where they occur. y = $C:\Users\john.morris\Desktop\f1q8g1.jpg$

		The minimum value is 0 at x = 1. The maximum value is 0 at x = -1.
		The minimum value is - 1 at x = -1. The maximum value is 1at x = 1.
		The maximum value is 0 at x = 0.
		The minimum value is 0 at x = 0.

4 points

QUESTION 16

· Find the absolute extreme values of the function on the interval. g(x) = 7 - 5x2, -3 ≤ x ≤ 5

		absolute maximum is 35 at x = 0; absolute minimum is -38 at x = -3
		absolute maximum is 5 at x = 0; absolute minimum is -132 at x = 5
		absolute maximum is 7 at x = 0; absolute minimum is -118 at x = 5
		absolute maximum is 14 at x = 0; absolute minimum is -38 at x = 5

4 points

QUESTION 17

· Find the absolute extreme values of the function on the interval. h(x) = $C:\Users\john.morris\Desktop\f1q19g9.jpg$ x + 4, -3 ≤ x ≤ 3

		absolute maximum is - $C:\Users\john.morris\Desktop\f1q21g2.jpg$ at x = -3; absolute minimum is $C:\Users\john.morris\Desktop\f1q21g2.jpg$ at x = 3
		absolute maximum is $C:\Users\john.morris\Desktop\f1q21g4.jpg$ at x = 3; absolute minimum is $C:\Users\john.morris\Desktop\f1q21g2.jpg$ at x = -3
		absolute maximum is - $C:\Users\john.morris\Desktop\f1q21g2.jpg$ at x = 3; absolute minimum is $C:\Users\john.morris\Desktop\f1q21g2.jpg$ at x = -3
		absolute maximum is - $C:\Users\john.morris\Desktop\f1q21g2.jpg$ at x = -3; absolute minimum is -3 at x = 3

4 points

QUESTION 18

· Determine all critical points for the function. f(x) = 20x3 - 3x5

		x = 2
		x = -2 and x = 2
		x = 0, x = -2, and x = 2
		x = -2

4 points

QUESTION 19

· Solve the problem. A baseball team is trying to determine what price to charge for tickets. At a price of $10 per ticket, it averages 45,000 people per game. For every increase of $1, it loses 5,000 people. Every person at the game spends an average of $5 on concessions. What price per ticket should be charged in order to maximize revenue?

		$13.00
		$4.00
		$3.00
		$7.00

4 points

QUESTION 20

· Solve the problem. Suppose c(x) = x3 - 24x2 + 30,000x is the cost of manufacturing x items. Find a production level that will minimize the average cost per item of making x items.

		12 items
		13 items
		14 items
		11 items

4 points

QUESTION 21

· Determine all critical points for the function. f(x) = x3 - 12x + 3

		x = -2 and x = 2
		x = -2, x = 0, and x = 2
		x = -2
		x = 2

4 points

QUESTION 22

· Determine all critical points for the function. y = 2x2 - 64 $C:\Users\john.morris\Desktop\f1q16g1.jpg$

		x = 0, x = 4, and x = -4
		x = 0 and x = 4
		x = 4
		x = 0

4 points

QUESTION 23

· Solve the problem. Of all numbers whose difference is 10, find the two that have the minimum product.

		1 and 11
		0 and 10
		20 and 10
		5 and -5

4 points

QUESTION 24

· Solve the problem. The stadium vending company finds that sales of hot dogs average 34,000 hot dogs per game when the hot dogs sell for $2.50 each. For each 50 cent increase in the price, the sales per game drop by 5000 hot dogs. What price per hot dog should the vending company charge to realize the maximum revenue?

		$0.90
		$2.95
		$3.20
		$3.40

4 points

QUESTION 25

· Determine all critical points for the function. f(x) = $C:\Users\john.morris\Desktop\f1q14g1.jpg$

		x = 8 and x = 0
		the function has no critical points
		x = 2
		x = 0 and x = -2