1 131201 Course MATH _: Section 4.1 1. What conditions must be met to ensue that a function has an absolute maximum vaIue and an absoIute minimum value on aninterva!? Choose the corect answer below. \"A, Thefunction must be continuous on a cIosed interval [a. ) B. The function must be continuous for some subinterval on [a,b]. C, Thefunction must be continuous on an open interval (a,b). D, A critical point must occu on a cIosed interval on [a,b]. 2" ldentify the graph of a function fthat has a IocaI Choose the corect graph beiow. maximum vaiue at x= b where f(b) is undefined. ) B, 3. How do you determine the absoIute maximum and minimum values ofa continuous function on a cIosed intervai? Choose the corect answer below. A"Evaluate the function at the criticai points. Choose the largest and smalIest vaIues ofthe function fo the absolute maximum and minimum values, reSPeCtivey, .B, EvaIuate the function at the critical points and at the endpoints ofthe cIosed interva=a,b]. Choose the largest and smailest vaiues of the function for the absoIute maximum and minimum vaiues, eSPeCtively. C, Evaluate the function at the endpoints ofthe cIosed interval [a,b]. Choose the Iargest and Sma=est values of the function fo the absoIute maximum and minimum values, eSPeCtiveiy. D EvaIuate the function at the citicaI points and at the endpoints ofthe open intervai (a,b). Choose the Iargest and smallest values of the function for the abso!ute maximum and minimum values, reSPeCtively. 4\"minemthe'g'aPhwhethethefunctionhasanyabso#eXtemeesqu ' . Where do the absolute extreme values ofthe function occur on a, b]? , A, Thee is no absoIute maximum and the absolute minimum occus atx=a On [a, b]. B, The absolute maximum occurs at x=d and the absolute minimum occurs at x=a Oa, b]. ) C, Thee is no absolute maximum and thee is no absolute minimum on [a, b]. D, The absolute maximum occus at x=d and there is no absolute minimum on [a, b]. 5. Use the graph to identify the points on the intervaI a,b] at Which local and absoIute extreme values occu. List the x-Values of the points whee local minima occuf any. Select the coect choice beiow andf necessay,in the answer box to complete your choice. ) A. The locaI minimum point(S) occu(S) at (Use a comma to sepaate answers as needed.) [) B. There are no 10Cal minima. List the x-Values of the points where locaI maxima occu, if any. Se!ect the corect choice below andf necessary,in the answer box to complete your choice. A, The local maximum point(S) occu(S) at X (Use a comma to sepaate answers as needed.) O B. Thereare no local maxima. ist the x-Values of the points where absoiute minima occur, if any. Select the corect choice below and, if necessary, jn the answe box to complete your choice. A. The absoIute minimum point(S) occur(S) atx= (Use a comma to separate answers as needed.) 1 B. Thee ae no absolute minima. ist the x-Values of the points where absolute maxima occur, if any SeIect the corect choice beIow andf necessary, in the answer box to compiete your choice. A,he absolute maximum point(S) occu(S) atx= (Use a comma to sepaate answers as needed.) B. Thee are no absolute maxima. 6. 1dentify the graph of a continuous function f on [0,8] satisfying the given poperties, f'is undefinedatx3and6; f'(4)=0;fhasaIocal maximum atx=3; fhasaIocal minimum atx=4;fhas an absolute maximum atx=6; and fhas an absolute mmum atx=8. Choose the correct gaph be!ow. 7. A stone is Ia...Ched vecally upward from a c128 ftabove the gound ata speed of l12 ft/s" lts heightabove the gound t seconds afterthe Iaunch is given by s= - 16t2 + 112t+ 128 for Ot8. When does the stone reach its maximum height? Find the derivative of s. I S The stone eaches its maximum height at s. (SimpIify your answer.) 8 Suppose a tourguide has a bus that holds a maximum of 82 peop!e. Assume his pofit (in do=ars)fortaking n people on a City tour is P(n) = n(41 - 0.5n) - 82 (Although P is defined onIy fo positive integers, treat it as a continuous function.) a" How many peopie should the guide take on a tou to maximize the profit? b" Suppose the bus hoIds a maximum of 37 people How many people shouId be taken on a tou to maximize the pro? a" Find the derivative of the given function P(n). P(n) !f the bus holds a maximum of 82 people, the guide should take people on a tou to maximize the profit. b" ifthe bus hoIds a maximum of 37 peopie, the guide should take peopIe on a tourto maximize the pofit