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Chapter l4-I! lnstructor:1|l Cource:re ---- Assignment: Chapter 14 Student:- Date: ID Find the locations of any absolute extrema for the function whose graph is shown to the right. At what x-coordinate, if any, does an absolute maximum occur? A. ce B. cr c. cz l:D.b E. No absolute maximum occurs. At what x-coordinate, if any, does an absolute minimum occur? No absolute minimum occurs. c1 ca a c2 What is the difference between a relative extremum and an absolute extremum? Choose the correct answer below. A continuous function on a closed interval can have more than one absolute maximum and absolute minimum but does not always have relative maximum and relative minimum' A continuous function on a closed interval can have more than one relative maximum and relative minimum but it has only one absolute maximum and absolute minimum. A continuous function on a closed interval can have more than one absolute maximum and absolute minimum but it has only one relative maximum and relative minimum. A continuous function on a closed interval can have more than one relative maximum and relative minimum but does not always have an absolute maximum and absolute minimum. A.

D- E.

D. 1 of6 - Chapter I4-III 3. Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x) = 2xa - 36x2 + 1 on the domain l- 4,41. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A- The absolute maximum is , which occurs at x = (Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.) B. There is no absolute maximum. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute minimum is , which occurs at x = (Round the absolute minimum to two decimal places as needed. Type an exact answer for the value of x where the minimum occurs. Use a comma to separate answers as needed.) B. There is no absolute minimum. 4. Find the absolute extrema if they exist, as well as all values of x where they occur, for the function 1 r. r5 f(x) = [x' - 16J on the domain t - 4,5] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice- A' The absolute maximum is , which occurs at x = (Round the absolute maximum to two decimal places as needed. Type an exaet answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.) B. There is no absolute maximum" Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. The absolute minimum is , which occurs at x = (Round the absolute minimum to two decimal places as needed. Type an exact answer for the value of x where the minimum occurs. Use a comma to separate answers as needed.) There is no absolute minimum. A, B. - 2of6 Chapter l4-ID 5. Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x)=2*2 - 16ln x on the domain [1,9]. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A- The absolute maximum is , which occurs at x = (Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.) B. There is no absolute maximum. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute minimum is , which occurs at x = (Round the absolute minimum to two decimal places as needed. Type an exact answer for the value of x where the minimum occurs. Use a comma to separate answers as needed.) B. There is no absolute minimum. GT 3 of 6 Chapter 14-IIID 6. The number of cups of coffee sold at Lauren's Coffee House for each week in November is shown in the graph at the right. Consider the closed interval [1,5] and give the relative and absolute extrema for the interval. a. ldentify each point as a relative minimum, a relative maximum, or neither. At week 1, 95 is a (1) At week 2,189 is a (2) At week 3, 298 is a (3) Atweek4, 191 isa (4) At week 5, 293 is a (5) b. For the interval [1,5], identify the absolute extrema and when they occur on the interval. c)d) oo@o"fO (2) (1) The absolute maximum is The absolute minimum is at week at week relative maximum relative minimum neither relative maximum relative minimum neither neither relative minimum relative maximum relative maximum neither relative minimum (3) neither relative minimum relative maximum (4) (5) 7. Foracertainautomobile, M(x)= -.015x2 +1.47x-7.8,30

mph. rI- Cups of Coffee Sold in November Weeks in November 4of6 (Type an integer or decimal rounded to the nearest thousandth as needed.) Chapter l4-lID 8. A campground owner has 1300 m of fencing. He wants to enclose a rectangular field bordering a river, with no fencing along the river. (See the sketch.) Let x represent the width of the field. (a) Write an expression for the length of the field as a function of x. (b) Find the area of the field (area = length xwidth) as a function of x. (c) Find the value of x leading to the maximum area. (d) Find the maximum area. (a) t(x; = River (b) A(x) = (c) First write the expression for the derivative used to find the x value that maximizes area. dA dx The x-value leading to the maximum area is (d) The maximum area of the rectangular plot is A local club is arranging a charter flight to Hawaii. The cost of the trip is $576 each for 85 passengers, with a refund of $5 per passenger for each passenger in excess of 85. a. Find the number of passengers that will maximize the revenue received from the flight. b. Find the maximum revenue. a. The number of passengers that will maximize the revenue received from the flight is (Round to the nearest integer as needed.) b. The maximum revenue is $ 10. A candy box is made from a piece of cardboard that measures 37 by 20 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box. What size square should be cut from each corner to obtain maximum volume? A square with a side of length inches should be cut away from each corner to obtain the maximum volume. (Round to the nearest hundredth as needed.) 11. A manufacturer has a steady annual demand for 22,638 cases of sugar. lt costs $7 to store 1 case for 1 year, $33 in set up cost to produce each batch, and $1 5 to produce each case. Find the number of cases per batch that should be produced to minimize cost. The manufacturer should produce (1) (2) (2) *u.

2m m. (1) 'n'2m m. 5 of6 (Round to the nearest whole number as needed.) cases per batch. II:} chaprer l4-- 12. A restaurant has an annual dennand for 922 bottles of California wine. lt costs $3 to store 1 bottle for 1 year, and it costs $6 to place a reorder. Find the optimum number of bottles per order. The optimum number of bottles per order is (Type a whole number.) 13. For the following demand function, find {a} E, and (b) values of q (if any) at which total revenue is maximized. p q=44_ i (a)E= (b) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. No values of q maximize the total revenue. B. The total revenue is maximized at q = 14. For the following demand function, find a. E, and b. the values of q (if any) at which total revenue is maximized. q=35,000-8p2 a. Determine the elasticity of demand, E. (Type an expression using p as the variable.) b. Determine the value of q that maximizes the revenue. Select the correct choice below, and if necessary, fill in the answer box within your choice. ' A. Total revenue is maximized at about q = (Round to the nearest whole number as needed.) B. No values of q maximize total revenue. -, 6 of6 Chapterz-IL n(B) = h'+4{\ comma to d ,4,5,6)rP6 P={1,3,4 answers as needed. List the elements in order with no duplicates.) Shade the Venn Diagram to show the set. cnD' Use the graphing toolto graph the set shading to show the following set on the Venn \m:;:,:* B)=44 and n(A) =24,what is n(B)? fy your answer.) 2ofl0 IED ChapterT-- fG) "o, are dealt one card from a standard S2-card deck. Find the probability of being dealt the three of diamonds. v The probability of being dealt the three of diamonds is (Type an integer or a simplified fraction.) f;) O card is drawn from a well-shuffled deck of 52 cards. Find the probability that the card is a red card or a 2. w, The probability is . (Type an integer or a simplified fraction.) ntain the chance of beillo seliltrdl lf from the box, what is the of drawing a cherry gumdrop? 0.1 an integer or a simplified fraction.) ts' 'of Find the probability of rolling a number greqler than 5. 6ofl0 -Ilr ChapterTilF For a medical experiment, people are classified as to whether they smoke, have a family history of sleep apnea, or are overweight. Define events E, F, and G, as shown below Complete parts a through c. E: person smokes F: person has a family history of sleep apnea G: person is overweight a. Describe the event G' in words. person (1) b. Describe the event F n G in words. person (2) (3) c. Describe the event E U G' in words. person (5) (4) (7) (6) (2) (1) is at their target weight is underweight is not underweight is not at their target weight is not overweight is overweight has a family history of sleeP apnea has no family history of sleep apnea smokes does not smoke (4) (3) (6) and or and (7) or is not at their target weight is not overweight is underweight is at their target weight is underweight is not underweight is not at their target weight is not overweight is ovenreight is not underweight is at their target weight is overweight (5) @ The following table gives the number of years of service of members in a certain committee. Find the probability that a randomly selected member of the committee had served 30-39 years. The probability that a randomly selected member had served for 30-39 years is (Type an integer or decimal rounded to the nearest hundredth as needed.) 21. Decide whether the mutually exc Years of Service 0-9 10-19 20-29 30-39 Number of Membes 56 26 16 2 0.02 the rTITT 7of10 a lhh school lly exclu being ChapterT{F @A pair of dice is rolled. Find the probability of rolling a) a sum not more than 4, b) a sum not less than 4, c) a sum between 5 and 10 (exclusive). a) The probability of rolling a sum not more than 4 is (Type an integer or a simplified fraction.) b) The probability of rolling a sum not less than 4 is (Type an integer or a simplified fraction.) c) The probability of rolling a sum between 5 and 10 (exclusive) i. _ (Type an integer or a simplified fraction.) between 0 and 1 the probabilities of 6 O single fair die is tossed. Find the odds in favor of rolling a number greater than 2. rJ What are the odds in favor of rolling a number greater than 2? to (Simplify your answer.) 24. An experiment is conducted for which the sample space is S = {s, ,sr,q,so,su}" ls the following probability possible for this experiment? -sr s2 s3 s4 ls the {A.

E. No, of the rules for an acceptable No the probabilities are given as decimals es, because both rules for an acceptable probability assignment not 1, assignment are satisfied. satisfied. .16 0.33 0.1 8ofl0 -F chapterTln The following table gives a future year's projected civilian labor force probability distribution by age and gender. Age Male Female Total 16-24 0.063 0.062 a.125 25-54 0.344 0.295 0.639 55 and over 0.128 0.108 0.236 Total 0.53s 0.465 1.00 Find the probability that a randomly selected worker is the following. (a) Male and 16 to 24 years old (b) 16 to 54 years old (c) Female or 25 to 54 years old (d) Male or 16 to 24 years old (a) The probability that a randomly selected worker is male and 16 to 24 years old is (Type an integer or a decimal.) (b) The probability that a randomly selected worker is 16 to 54 years old is (Type an integer or a decimal.) (c) The probability that a randomly selected worker is female or 25 to 54 years old is (Type an lnteger or a decimal.) (d) The probability that a randomly selected worker is male or 16 to 24 years old is (Type an integer or a decimal.) @ turpose a single fair die is rolled. Find the probability that it is a 2, given that it is an odd number. The probability is (Type an integer or a simplified fraction.) (E ,*o cards are drawn without replacement from an ordinary deck. Find the probability that the second is a V face card, given that the first is a king. The probability is (Simplify your answer. Type an integer or a simplified fraction.) whether the following pair of events are dependent or independent. event that a of New York York City, and F is the event that a resident of in either or lndependent 9of10 NIFI Chapter 7-ll!!l 29. The given table indicates the transactions at a bank for one teller for one day. Letting C represent "cashing a check" and D represent "making a deposit," express P (C'lD) in words and find its value. The table shows frequencies for red-green color blindness, where M represents "person is male" and C represents "person is color-blind." Use this table to find P(Mlc). Transaction Cash Check No Check Totals Make Deposit No Deposit Totals 53 27 80 30 13 43 83 40 123 Express P (C'lD) in words. f A. The probability of a customer not cashing a check, given that the customer makes a deposit B. The probability of a customer not making a deposit, given that the customer cashed a check. C. The probability of a customer not cashing a check, given that the customer does not make a deposit D. The probability of a customer cashing a check, given that the customer makes a deposit Find P (C'lD) . x P (c'lD) = 0.36 (Type an integer or decimal rounded io two decimal places as needed.) YOU ANSWERED: 1 8 M M' Totals c c' Totals 0.038 0.s05 0.543 0.004 0.453 4.457 0.042 0.958 1.000 31. P(MlC)= (Round to three decimal places, as needed.) A has found that the probability that a student studies for a test is 0.71, and the probability that a student gets a a. Are grade on a test is 0.55, and the probability that both occur is 0.45. independent? b. Given that studies, find the probability that the student gets a good grade. c. Given that a gets a good grade, find the probability that the student a. Are these events i *No Yes b. Given that a student studies, the student gets a good grade is (Type an integer or decimal rounded to tw-o, places as needed.) c. Given that a student gets a , the that the student studied is (Type an integer or decimal 0.63 .,{ a.82 ffi, 0.78 l0 of l0 YOU to two decimal as needed.)