Home H Week 7 "Applications of Differentiation" Courses James Rhoads ? Take Test: W7 Practice Take Test: W7 Practice Test Information Description Instructions Multiple Attempts This test allows multiple attempts. Force Completion This test can be saved and resumed later. Question Completion Status: Save All Answers Q U E S T I O N 1 Save and Submit 0 points Saved Determine all critical points for the function. f(x) = x3 9x2 + 1 x = 3 and x = 3 x = 0 x = 0 and x = 3 x = 0 and x = 6 Q U E S T I O N 2 0 points Save Answer Solve the problem. A piece of molding 163 cm long is to be cut to form a rectangular picture frame. What dimensions will enclose the largest area? 32.6 cm 32.6 cm 40.75 cm 40.75 cm 12.77 cm 12.77 cm 12.77 cm 40.75 cm Q U E S T I O N 3 0 points Save Answer Solve the problem. Recent research has shown that the population f(S) of cod in the North Sea next year as a function of this years population S (measured in thousands of tons) can be described by the Shepherd model, f(S) = where a, b, and c are constants. The values of a, b, and c are 3.039, 247, and 3.25, respectively. Find the approximate value of this years population that maximizes next years population using this model. 158,000 tons 4000 tons 192,000 tons 192 tons Q U E S T I O N 4 0 points Save Answer Find the absolute extreme values of the function on the interval. f(x) = |x 2|, 1 x 5 absolute maximum is 1 at x = 1; absolute minimum is 0 at x = 2 absolute maximum is 1 at x = 1; absolute minimum is 3 at x = 5 absolute maximum is 3 at x = 5; absolute minimum is 1 at x = 1 absolute maximum is 3 at x = 5; absolute minimum is 0 at x = 2 Q U E S T I O N 5 0 points Saved Find the extreme values of the function and where they occur. y = x3 12x + 2 Local maximum at (2, 18), local minimum at (2, 14). Local maximum at (2, 14), local minimum at (2, 18). None Local maximum at (0, 0). Q U E S T I O N 6 0 points Save Answer Solve the problem. Find two numbers x and y such that their sum is 420 and x2y is maximized. x = 140, y = 280 x = 280, y = 140 x = 105, y = 315 x = 315, y = 105 Q U E S T I O N 7 0 points Save Answer 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 prot? $102 $202 $192 $190 Q U E S T I O N 8 Solve the problem. An architect needs to design a rectangular room with an area of 80 ft2. What dimensions should he use in order to minimize the perimeter? 20 ft 20 ft 8.94 ft 8.94 ft 8.94 ft 20 ft 16 ft 80 ft 7 Content Collection 0 points Save Answer 0 points Save Answer Q U E S T I O N 9 Find the extreme values of the function and where they occur. y = The maximum value is 1 at x = 0. The minimum value is 1 at x = 0.5. The maximum 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. 0 points Save Answer Q U E S T I O N 1 0 Find the extreme values of the function and where they occur. y = Question Completion Status: Local maximum at (1, 0), local minimum at (1,0). None Local maximum at (0, 1). Local maximum at (1, 0), local minimum at (1, 0). 0 points Save Answer Q U E S T I O N 1 1 Solve the problem. A rectangular eld is to be enclosed on four sides with a fence. Fencing costs $4 per foot for two opposite sides, and $7 per foot for the other two sides. Find the dimensions of the eld of area 830 ft2 that would be the cheapest to enclose. 16.5 ft @ $4 by 50.4 ft @ $7 38.1 ft @ $4 by 21.8 ft @ $7 21.8 ft @ $4 by 38.1 ft @ $7 50.4 ft @ $4 by 16.5 ft @ $7 0 points Save Answer Q U E S T I O N 1 2 Find the absolute extreme values of the function on the interval. f(x) = csc x, x absolute maximum does not exist; absolute minimum does not exist absolute maximum is 1 at x = ; absolute minimum is 1 at x = absolute maximum is 1 at x = ; absolute minimum is 1 at x = 0 absolute maximum is 0 at x = ; absolute minimum is 1 at x = 0 points Save Answer Q U E S T I O N 1 3 Solve the problem. If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a certain city, where p(x) = 127 . How many candy bars must be sold to maximize revenue? 2159 thousand candy bars 4318 thousand candy bars 4318 candy bars 2159 candy bars 0 points Save Answer Q U E S T I O N 1 4 Determine all critical points for the function. f(x) = x3 12x + 3 x = 2 x = 2, x = 0, and x = 2 x = 2 x = 2 and x = 2 0 points Save Answer Q U E S T I O N 1 5 Find the absolute extreme values of the function on the interval. f(x) = tan x, x absolute maximum is 1 at x = and ; absolute minimum does not exist absolute maximum is 1 at x = ; absolute minimum is 1 at x = absolute maximum is 1 at x = ; absolute minimum is 1 at x = absolute maximum is 1 at x = ; absolute minimum is 1 at x = 0 points Save Answer Q U E S T I O N 1 6 Find the absolute extreme values of the function on the interval. g(x) = x2 + 10x 21, 3 x 7 absolute maximum is 4 at x = 6; absolute minimum is 0 at 7 and 0 at x = 3 absolute maximum is 5 at x = 6; absolute minimum is 0 at 7 and 0 at x = 3 absolute maximum is 4 at x = 5; absolute minimum is 0 at 7 and 0 at x = 3 absolute maximum is 46 at x = 5; absolute minimum is 0 at 7 and 0 at x = 3 0 points Save Answer Q U E S T I O N 1 7 Find the extreme values of the function and where they occur. y = x2 + 2x 3 The minimum is 4 at x = 1. The minimum is 1 at x = 4. The minimum is 1 at x = 4. The minimum is 1 at x = 4. 0 points Save Answer Q U E S T I O N 1 8 Find the absolute extreme values of the function on the interval. f() = sin , 0 f() = sin , 0 absolute maximum is 1 at = 0; absolute minimum is 1 at = absolute maximum is 1 at = ; absolute minimum is 1 at = , absolute maximum is 1 at = ; absolute minimum is 1 at = , absolute maximum is 1 at = ; absolute minimum is 1 at = 0 points Save Answer Q U E S T I O N 1 9 Find the extreme values of the function and where they occur. y = x3 3x2 + 1 None Local maximum at (0, 1). Local minimum at (2, 3). Local maximum at (0, 1), local minimum at (2, 3). Question Completion Status: 0 points Save Answer Q U E S T I O N 2 0 Determine all critical points for the function. f(x) = x2 + 12x + 36 x = 0 x = 6 x = 12 x = 6 0 points Save Answer Q U E S T I O N 2 1 Solve the problem. If the price charged for a bolt is p cents, then x thousand bolts will be sold in a certain hardware store, where . How many bolts must be sold to maximize revenue? 259 thousand bolts 259 bolts 518 bolts 518 thousand bolts Q U E S T I O N 2 2 0 points Save Answer Find the absolute extreme values of the function on the interval. f(x) = 2x 1, 2 x 4 absolute maximum is 9 at x = 4; absolute minimum is 3 at x = 2 absolute maximum is 7 at x = 4; absolute minimum is 5 at x = 2 absolute maximum is 9 at x = 4; absolute minimum is 5 at x = 2 absolute maximum is 7 at x = 2; absolute minimum is 3 at x = 4 Q U E S T I O N 2 3 0 points Save Answer Solve the problem. Find two numbers whose sum is 490 and whose product is as large as possible. 245 and 245 10 and 480 1 and 489 244 and 246 Q U E S T I O N 2 4 0 points Save Answer Solve the problem. Find the dimensions that produce the maximum oor area for a onestory house that is rectangular in shape and has a perimeter of 148 ft. 12.33 ft 37 ft 37 ft 148 ft 74 ft 74 ft 37 ft 37 ft Q U E S T I O N 2 5 0 points Save Answer Solve the problem. A company wishes to manufacture a box with a volume of 40 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material. 3.2 ft 3.6 ft 6.4 ft 7.2 ft Click Save and Submit to save and submit. Click Save All Answers to save all answers. Save All Answers Save and Submit Home H Week 7 "Applications of Differentiation" Courses James Rhoads Content Collection ? Take Test: W7 Quiz X You recently left the test ''W7 Quiz'' without submitting it. Return to the test and click Save and Submit or contact your instructor for assistance. Take Test: W7 Quiz Test Information Description Instructions Multiple Attempts Not allowed. This test can only be taken once. Force Completion This test can be saved and resumed later. Question Completion Status: Save All Answers Save and Submit 4 points Save Answer Q U E S T I O N 1 Find the absolute extreme values of the function on the interval. F(x) = , 0.5 x 4 absolute maximum is at x = absolute maximum is at x = 4; absolute minimum is 4 at x = absolute maximum is ; absolute minimum is 4 at x = 4 at x = ; absolute minimum is 4 at x =4 absolute maximum is at x = 4; absolute minimum is 4 at x = 4 points Save Answer Q U E S T I O N 2 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 prot? $102 $202 $190 $192 4 points Save Answer Q U E S T I O N 3 Solve the problem. Maximize Q = xy2, where x and y are positive numbers, such that x + y2 = 10. x = , y = 5 x = 0, y = x = 1, y = 3 x = 5, y = 4 points Save Answer Q U E S T I O N 4 Solve the problem. The stadium vending company nds 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 $3.40 $3.20 4 points Save Answer Q U E S T I O N 5 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 11 items 14 items 13 items 4 points Save Answer Q U E S T I O N 6 Find the extreme values of the function and where they occur. y = 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 = 0.5. The maximum value is 1 at x = 0. 4 points Save Answer Q U E S T I O N 7 Determine all critical points for the function. f(x) = x3 12x + 3 x = 2, x = 0, and x = 2 x = 2 and x = 2 x = 2 x = 2 4 points Save Answer Q U E S T I O N 8 Find the extreme values of the function and where they occur. y = x3 3x2 + 4x 4 The minimum is 0 at x = 1. None The maximum is 0 at x = 2. The maximum is 0 at x = 1. 4 points Save Answer Q U E S T I O N 9 Find the absolute extreme values of the function on the interval. h(x) = x + 4, 3 x 3 absolute maximum is at x = 3; absolute minimum is at x = 3 absolute maximum is at x = 3; absolute minimum is 3 at x = 3 absolute maximum is at x = 3; absolute minimum is at x = 3 absolute maximum is at x = 3; absolute minimum is at x = 3 4 points Save Answer Q U E S T I O N 1 0 Find the extreme values of the function and where they occur. y = The minimum is 0 at x = 1. The maximum is 6 at x = 2. The minimum is 6 at x = 0. The maximum is 6 at x = 2. 4 points Save Answer Q U E S T I O N 1 1 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 0 at x = 0 absolute maximum is 3 at x = 1 ; absolute minimum is 0 at x = 0 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 4 points Save Answer Q U E S T I O N 1 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 Save Answer Q U E S T I O N 1 3 Find the extreme values of the function and where they occur. y = The maximum is 3 at x = 0; the minimum is at x = 2. The maximum is at x = 0; the minimum is 1 at x = 2. The maximum is at x = 0; the minimum is 1 at x = 2. None Q U E S T I O N 1 4 4 points Save Answer Find the absolute extreme values of the function on the interval. F(x) = , 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 Q U E S T I O N 1 5 4 points Save Answer Find the absolute extreme values of the function on the interval. g(x) = 7 5x2, 3 x 5 absolute maximum is 14 at x = 0; absolute minimum is 38 at x = 5 absolute maximum is 7 at x = 0; absolute minimum is 118 at x = 5 absolute maximum is 5 at x = 0; absolute minimum is 132 at x = 5 absolute maximum is 35 at x = 0; absolute minimum is 38 at x = 3 Q U E S T I O N 1 6 4 points Save Answer Solve the problem. Of all numbers whose dierence is 10, nd the two that have the minimum product. 0 and 10 5 and 5 1 and 11 20 and 10 Q U E S T I O N 1 7 4 points Save Answer 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 Q U E S T I O N 1 8 Solve the problem. 4 points Save Answer 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? $3.00 $7.00 $13.00 $4.00 4 points Save Answer Q U E S T I O N 1 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 does not exist 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 is 1 at x = 1 4 points Save Answer Q U E S T I O N 2 0 Question Completion Status: Determine all critical points for the function. f(x) = the function has no critical points x = 8 and x = 0 x = 2 x = 0 and x = 2 4 points Save Answer Q U E S T I O N 2 1 Find the absolute extreme values of the function on the interval. f(x) = tan x, x absolute maximum is 1 at x = ; absolute minimum is 1 at x = absolute maximum is 1 at x = ; absolute minimum is 1 at x = absolute maximum is 1 at x = and absolute maximum is 1 at x = ; absolute minimum does not exist ; absolute minimum is 1 at x = Q U E S T I O N 2 2 4 points Save Answer Find the extreme values of the function and where they occur. y = (x 4)2/3 The maximum value is 0 at x = 4. The minimum value is 0 at x = 4. There are no denable extrema. The minimum value is 0 at x = 4. Q U E S T I O N 2 3 4 points Save Answer Determine all critical points for the function. f(x) = (x 10)5 x = 10 and x = 5 x = 0, x = 10, and x = 5 x = 0 and x = 10 x = 10 Q U E S T I O N 2 4 4 points Save Answer Determine all critical points for the function. y = 2x2 64 x = 4 x = 0 x = 0 and x = 4 x = 0, x = 4, and x = 4 Q U E S T I O N 2 5 4 points Save Answer Find the extreme values of the function and where they occur. y = The maximum value is 0 at x = 0. The minimum value is 1 at x = 1. The maximum value is 1at x = 1. The minimum value is 0 at x = 1. The maximum value is 0 at x = 1. The minimum value is 0 at x = 0. Click Save and Submit to save and submit. Click Save All Answers to save all answers. Save All Answers Save and Submit