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# Ex 3_3 - D 3.3 T he erivative a R ate f C hange as o 1 53...

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3.3 The Derivative as a Rate of Change 153 Sotution Thc cost o I producnrg onc more radiator a day whenI 0 arc produced is aboul .'(10): ,, ' ;, l r' o., l<,' .'r' - l2r - ls .'(10) = 3(r00) r2(r0) + r5 : 195. The additional cost wiLl be aboxt \$195. The narginal relerueis hr + r2r):3.rr 6.'+ 12. The marginalrevenue llnclion cslinratcs thc increase in revenue that sill rcsult from sell- ing on€ additional unit. Ilyou currcnll) scll l0 radiabrs a day. you can expect your rev enue to rncrease by about r'(10) = 3(100) 6(10) + 12 : \$252 ifyou increase sales lo i1 rrdiators.r d.rt. bracket and your margin.tlrate will increase. - fta' EXAM P LE 6 To gct sonc feel for the language of maryinalrates. consider marginal tax ralcs. Ifyouf marginal inconc tax ralc is 28% and your income increases by \$1000, you can expect 1() pay an exra \$280 in t.txcs. This does not mean that you pay 28% ofyour en- dre lncone ln laxes. Il jusr mcans that at your current income level /, the rute ofincrease of taxcs Iwith rcspccl to incamc is dT/dI : 0.28. You \rill pay \$0.28 out of every extra dol- la. you cdrn in taxcs. Of course. if you earn a lot more, you may land in a higher tax EXERCISES 3.3 l :::.,!es I 6 gnc thc positions r = /(, of a body moune on a coor :r,:r line, wirh r in nrete.s and rii scconds. ^ F,nd thc body\ dislhcemert ard average velocity for thegiven b- Frndthc bodys speed ed acceleratior at theeldpoinlsofthe :. \!hcn, ifever, duriry theinterval does lhebody change direc r.,=r: 3r+2.0<r=2 :.=ar rr,0</<6 r..= t+3/: lr o</<.1 r.,=(/1/4) rr+1. 0</<3 ..=?i ! ,=,-. 25 -_ 4<t<u -. Particle motion At time r. the posidon ofa body movinS alory rhcldhisi=r' 6rt+9/m a. fild lhebody's .ccelemtion each tnne the velocity is zero. b. Find tlc body\ spc.d cach timc thc accclcrarion is zcrc. c, liM thc rotal distmce tra\rled by rhc body ftom r = 0 ro t=2.

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Ex 3_3 - D 3.3 T he erivative a R ate f C hange as o 1 53...

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