math2 - "#$&" 012%3%4...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: !"#$%&'(%%)*+#%,%%%%%%%%%%%%%%%%%%%%-".*////////////////////////% %%%%%%%%%%% 012)%3%4%15+678#*%!"9:.8.;!:<:.8.%0=657*.+>%%% ! "#!$%&'!()*!+,-./0(*!1+2%101!+&'!1%&%101!.3! f ( x) # x 3 " 3 x 2 " 24 x ! 5 .&!()*!%&(*45+/!6789:;#! f $( x) # 3x 2 " 6 x " 24 f ("3) # 23 0 # 3x 2 " 6 x " 24 f ("2) # 33 0 # 3( x 2 " 2 x " 8) ! f (4) # "75 0 # 3( x " 4)( x ! 2) f (6) # "31 x # 4,"2 ! <,-./0(*!1+2%101!5+/0*!=!88!!>)*&!2!=!7?! ! <,-./0(*!1%&[email protected]!>)*&!2!=!B! ! ! ?#!$%&'!()*!+,-./0(*!1+2%101!+&'!1%&%101!.3! f ( x) # x 4 " 32 x 2 " 7 .&!()*!%&(*45+/!6C9:;#! f $( x) # 4 x 3 " 64 x 0 # 4 x 3 " 64 x 0 # 4 x( x " 16) 0 # 4 x( x ! 4)( x " 4) 2 f (0) # "7 f (4) # "263 ! f (6) # 137 x # 0,"4,4 ! <,-./0(*!1+2%101!5+/0*!=!"8@!!>)*&!2!=!:! ! <,-./0(*!1%&%101!5+/0*!=!7?:8!>)*&!2!=!B! ! ! ! 8#!$%&'!()*!+,-./0(*!1+2%101!+&'!1%&%101!.3! f ( x) # ( x " 3)( x ! 6) 2 !.&!()*!%&(*45+/!67:9?;#!D.(*! ()+(! f ' ( x ) # ( x ! 6)(3 x ) #! f ( x) # ( x " 3)( x ! 6) 2 f $( x) # ( x " 3)(2)( x ! 6) ! ( x ! 6) 2 f $( x) # ( x ! 6)(( x " 3)(2) ! ( x ! 6)) f $( x) # ( x ! 6)(3x) 0 # ( x ! 6)(3x) x # "6,0 ! <,-./0(*!1+2%101!5+/0*!=!C!!>)*&!2!=!7:! ! <,-./0(*!1%&%101!5+/0*!=!7"CE!>)*&!2!=!C! f ("6) # 0 f (0) # "108 ! f (2) # "64 012)%&%4%?@#:.:A"#:6<%0=657*.+%BC*D#:6<%'>&E>%! B#!!$%&'!()*!'%1*&-%.&-!.3!()*!4*F(+&G0/+4!3%*/'!.3!1+2%101!+4*+!()+(!F+&!,*!1+'*!34.1!:B1!.3! 3*&F%&G#!!H>.!+''%(%.&+/!3*&F*-!+4*!&**'*'!+F4.--!%(-!>%'()9!+-!-).>&!%&!()*!-I*(F)#! F!0?2)1-)J!K-*!()*!5+4%+,/*-!2!+&'!L!+-!'*3%&*'!%&!()*!M4.,/*1!+&'!.&!()*!3%G04*#!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ! ! ! ! ! ! ! ! !!!!!!!!!! P # 4 x ! 2 y # 64 2 y # 64 " 4 x !!!!!!!!N!!!!! 64 " 4 x y# 2 y # 32 " 2 x !!!!!! A # xy A # x(32 " 2 x) A # 32 x " 2 x 2 A$ # 32 " 4 x A # x(32 " 2 x) A # 8(32 " 2(8)) A # 128 m 2 A # xy 0 # 32 " 4 x x #8 A$$ # "4 % 0 !!! 128 # 8 y ! y # 16 H)*!1+2!+4*+!%-!"?E!1?!!>)*&!()*!'%1*&-%.&-!+4*!2!=!E!,L!L!=":#! ! A#!!$%&'!(>.!&.&&*G+(%5*!&01,*4-!2!+&'!L!3.4!>)%F)! 2 x ! y # 30, !-0F)!()+(! x 2 y !%-!1+2%1%P*'#! H)*!1+2%101!%-!"CCC!>)*&!2=!"C!!+&'!L="C#!!!! ! z # x2 y !!!!!!!!!!O!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! z # x 2 (30 " 2 x) 2 x ! y # 30 !!!!!!!!! z $ # 60 x " 6 x 2 y # 30 " 2 x on [0,15] 0 # 60 x " 6 x 2 z # 30 x 2 " 2 x 3 0 # 6 x(10 " x) x # 0,10 z ( x) # x 2 (30 " 2 x) 2(10) ! y # 30 z (0) # 0 !!!!!!!!!!! !!!!! ! y # 10 z (10) # 1000 z (15) # 0 ! :#!Q3!()*!M4%F*!F)+4G*'!3.4!+!F*4(+%&!F+&'L!,+4!%-! p(x) F*&(-9!()*&!2!().0-+&'!F+&'L!,+4-!>%//!,*! x #! -./'!%&!+!F*4(+%&!F%(L9!>)*4*! p ( x) # 200 " 20 x p ( x) # 200 " R( x) # 200000 x " 50 x 2 20 R$$( x) # "100 % 0, so a rel. max occurs R ( x) # 1000 xp R $( x) # 200000 " 100 x !!!!!! !! ! x 0 # 200000 " 100 x R ( x) # 1000 x(200 " ) R( 2000 ) # $200,000,000 20 x # 2000 R ( x) # 200000 x " 50 x 2 ! ?CCC!!+#!$%&'!()*!5+/0*!.3!2!()+(!/*+'-!(.!+!1+2%101!4*5*&0*#! ! R?CC9CCC9CCC!,#!!$%&'!()*!1+2%101!4*5*&0*#!! ! 012)%G%4%F.@7:D:#%H:II*=*<#:"#:6<>%%% S%4*F(%.&-J!!K-*!%1M/%F%(!'%33*4*&(%+(%.&!(.!3%&'!LT#!!U).>!*+F)!-(*M!F/*+4/L!+&'!,.2!%&!L.04!3%&+/! +&->*4#% ! @#! 3 y 4 " 5 x ! y # 17 ! 3 y 4 " 5 x ! y # 17 ! ! 12 y 3 dy dy "5! #0 ! dx dx dy (12 y 3 ! 1) # 5 dx dy 5 # ! dx 12 y 3 ! 1 ! E#! x 2 ! 2 xy " y 3 # 4 x ! x 2 ! 2 xy " y 3 # 4 x d 2 d d d ( x ) ! (2 xy ) " ( y 3 ) # (4 x) dx dx dx dx d 2 d d d d ( x ) ! 2 x ( y ) ! y (2 x) " ( y 3 ) # (4 x) dx dx dx dx dx ! dy dy #4 2x ! 2x ! 2 y " 3 y 2 dx dx dy # 4 " 2x " 2 y (2 x " 3 y 2 ) dx dy 4 " 2 x " 2 y # ! dx 2x " 3y 2 ! ! ! V#! e 3y ! # x ! 4 y !1! e3 y # x ! 4 y ! 1 ! ! 3e 3 y ! ! dy dy #1! 4 dx dx ! dy (3e 3 y " 4) #1 dx dy 1 # 3y ! dx 3e " 4 ...
View Full Document

This test prep was uploaded on 04/17/2008 for the course MATH 267 taught by Professor K during the Spring '08 term at Ole Miss.

Ask a homework question - tutors are online