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# tutorial 9 solutions

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Depart*reni of Mathematics a'cl Applied fulabirenraticsAYl/g MAM104F Tutorial Solutions ftrtJ 2t:6-- 1. (a) Maximize the area, fionnula; .21 2rU,Ihus - (b) By Pythagolas, :1'2, -p 12 y (F i. so !J2 we set' : A(r;) zr({F-: rz1.in problem, this rve must think of'r. being fixecl; il'it weren,t fixerl,there would be no possibie answer for the problenr, so we reallydo have a fo'nula for ,4 in tel'rs of the one variable r.(c) bbr critical points, find A,(r):- : A'(r) z(\/ra - r\ (zr)*t + (-2:r),r)-i - ,rz - : -Jt-:2/P * s2{r'2 It helps put to everything ovel' a cornfiron cleiror'inator, sojx - 4r2=2/F1EW* -zr2 A,(d - -m'az {r2 1F You can factoriz,c the nurnerator'. so)(,. _ _F --:--;;:__---::t.{2t)1, /i)' - .4'(r) The critical poirrbs : -#, will occur : at, r and * Clearlyft the negative value for r rnahes no senJq sirrce thai #Julcl ,r1plythat our area is negative too; uo such thing as negative area, Tleonly sensible poinb critical : then is n ft.(d) You couid find the secoucl clelivative of ;1, bur quite bhat's rnessy.(Do it il' you are boled!) I3ut we cau see, fronr the factorizedversion ctl rl'(:r) thab A'(e-) chauges fi'orn being positive it r < frto negative if r , (The olly facbor that, plays any role iniE. - tlris discussion is ttre factor (, the other {2*); two I'acLols arepositive definitelv positive for z.) This means zl increases forr < and decreases for n > we thus have a maximurn forft ft. - A a,L r This finishes the'p'oblem more or ...

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 Publié par Shean Nombre de lectures 8 Langue English

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