H Week 7 "Applications of Differentiation" Take Test: W7 Quiz 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. 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 minimum does not exist absolute maximum is 1 at x = ; absolute minimum is ­1 at x = ­ QUESTION 1 4 points Save Answer Find the absolute extreme values of the function on the interval. f(x) = 3x 2/3, ­27 ≤ 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 27 at x = ­27 ; absolute minimum is 3 at x = 1 absolute maximum is 3 at x = 1 ; absolute minimum is 0 at x = 0 QUESTION 2 4 points Save Answer Determine all critical points for the function. f(x) = x 3 ­ 12x + 3 x = 2 x = ­2 x = ­2 and x = 2 x = ­2, x = 0, and x = 2 QUESTION 3 4 points Save Answer Solve the problem. Of all numbers whose difference is 10, find the two that have the minimum product. 5 and ­5 1 and 11 20 and 10 0 and 10 QUESTION 4 4 points Save Answer Solve the problem. Maximize Q = xy 2, where x and y are positive numbers, such that x + y 2 = 10. x = 1, y = 3 x = , y = 5 x = 0, y = x = 5, y = QUESTION 5 4 points Save Answer 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. 3.3 in. by 3.3 in. by 3.3 in.; 37 in.3 6.7 in. by 6.7 in. by 3.3 in.; 148.1 in.3 5 in. by 5 in. by 2.5 in.; 62.5 in.3 6.7 in. by 6.7 in. by 1.7 in.; 74.1 in.3 QUESTION 6 4 points Save Answer Find the absolute extreme values of the function on the interval. f(x) = x 4/3, ­1 ≤ x ≤ 8 absolute maximum is 16 at x = 8; absolute minimum is 1 at x = ­1 absolute maximum is 64 at x = 8; absolute minimum is 0 at x = 01 absolute maximum is 16 at x = 8; absolute minimum is 0 at x = 01 absolute maximum is 16 at x = 8; absolute minimum does not exist QUESTION 7 4 points Save Answer Find the extreme values of the function and where they occur. y = x 3 ­ 3x 2 + 4x ­ 4 The minimum is 0 at x = ­1. The maximum is 0 at x = 2. None The maximum is 0 at x = 1. QUESTION 8 4 points Save Answer 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 QUESTION 9 4 points Save Answer Find the absolute extreme values of the function on the interval. F(x) = , ­2 ≤ x ≤ 8 absolute maximum is 2 at x = 8; absolute minimum is ­2 at x = ­8 absolute maximum is 2 at x = 8; absolute minimum is 0 at x =0 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 QUESTION 10 4 points Save Answer Find the extreme values of the function and where they occur. y = The minimum value is 0 at x = 1. The maximum value is 0 at x = ­1. The minimum value is 0 at x = 0. The minimum value is ­ 1 at x = ­1. The maximum value is 1at x = 1. The maximum value is 0 at x = 0. QUESTION 11 4 points Save Answer ? Question Completion Status: Home Courses Click Save and Submit to save and submit. Click Save All Answers to save all answers. Save All Answers Save and Submit Stephanie Townsend The maximum value is 0 at x = 0. 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. The maximum value is 1 at x = 0.5. QUESTION 12 4 points Save Answer Determine all critical points for the function. f(x) = x = 2 x = 0 and x = ­2 the function has no critical points x = 8 and x = 0 QUESTION 13 4 points Save Answer Determine all critical points for the function. y = 2x 2 ­ 64 x = 4 x = 0 x = 0 and x = 4 x = 0, x = 4, and x = ­4 QUESTION 14 4 points Save Answer Find the extreme values of the function and where they occur. y = The maximum is at x = 0; the minimum is ­ 1 at x = ­2. The maximum is 3 at x = 0; the minimum is at x = ­2. None The maximum is ­ at x = 0; the minimum is 1 at x = ­2. QUESTION 15 4 points Save Answer Solve the problem. Suppose c(x) = x 3 ­ 24x 2 + 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. 11 items 12 items 14 items 13 items QUESTION 16 4 points Save Answer Find the extreme values of the function and where they occur. y = The maximum is 6 at x = ­2. The minimum is 0 at x = 1. The minimum is 6 at x = 0. The maximum is 6 at x = 2. QUESTION 17 4 points Save Answer 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 at 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 QUESTION 18 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. The minimum value is 0 at x = ­4. There are no definable extrema. QUESTION 19 4 points Save Answer Find the absolute extreme values of the function on the interval. F(x) = ­ , 0.5 ≤ x ≤ 4 absolute maximum is ­ at x = 4; absolute minimum is ­4 at x = absolute maximum is ­ at x = ; absolute minimum is ­4 at x = ­4 absolute maximum is at x = ; absolute minimum is ­4 at x =4 absolute maximum is ­ at x = 4; absolute minimum is ­4 at x = ­ QUESTION 20 4 points Save Answer 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? $3.20 $3.40 $0.90 $2.95 QUESTION 21 4 points Save Answer Determine all critical points for the function. f(x) = 20x 3 ­ 3x 5 x = ­2 x = ­2 and x = 2 x = 0, x = ­2, and x = 2 x = 2 QUESTION 22 4 points Save Answer Find the absolute extreme values of the function on the interval. g(x) = 7 ­ 5x 2, ­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 QUESTION 23 4 points Save Answer Question Completion Status: Click Save and Submit to save and submit. Click Save All Answers to save all answers. Save All Answers Save and Submit 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 $7.00 $4.00 $3.00 QUESTION 24 4 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 profit? $202 $102 $192 $190 QUESTION 25 4 points Save Answer Question Completion Status: Click Save and Submit to save and submit. Click Save All Answers to save all answers. Save All Answers Save and Submit

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