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Problem 3 of MIDTERM Page #9 Group 6 Ritchie Roi Chua Ramon Jose Miguel Naguiat Mary Jane L. Paglumotan Mark Anthony Salazar Mark Anthony Salazar Charlotte Tang Tong Ya(Nicole)

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Problem 3 (Page 289 #9) A research organization made a survey of the listening habits of the residents in a certain population between 4pm and midnight. The survey reveals that the fraction of the adult population that listens to a particular radio station X hours after 4pm is given by F(X)= -2X X X A. A.At what time between 4pm and midnight are the most people listening to the station? B. B.At what time between 4pm and midnight are the least people listening to the station?

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Solution F(X)=-2X 3 +27X X+300 to get the critical points: F’(X)= -6X 2 +54X-108 F’(X)= 0 -6X 2 +54X-108=0 6X 2- 54X+108=0 6(X 2- 9X+18)=0 X 2- 9X+18=0 (X-3)(X-6)=0 X=3 and X=6 at X=3,Y=192 at X=6, Y=165

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Solution To Check whether X=3 and X=6 are min/max points: F”(X)=-12X+54 At X=6: F”(X)=-12(6)+54=-18 F”(X)<0 therefore F(X) is a MAXIMUM at X=6 At X=3: F”(X)=-12(3)+54=18 F”(X)>0 therefore F(X) is a MINIMUM at X=3

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Conclusion A. The time wherein the MOST people are listening to the station is 10 pm =4pm+X hours =4+6=10pm B. The time wherein the LEAST people are listening to the station is 7 pm =4pm+X hours =4+3=7pm

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Graph X=-2X 3 +27X X+300 X = 3 ; 7pm X = 6 ; 10 pm

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Web Links max-min.pdf max-min.pdf max-min.pdf rema.htm rema.htm rema.htm maxmin.html maxmin.html maxmin.html

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