You eed to kow: Rolle s Theoem: f ) f is cotiuous o [.bj, 2) f is diffeetible o (,b), d ) f()=f(b), the thee s oe c i (,b) whee f (c) = Me Vlue Theoem: l) f is cotiuous o [.b d 2) f is diffeetible o (,b), the thee s t lest to of the ldde isig t the momet the bottom is 5 feet fom the wll? icesig whe the dius is 6 iches? llel to the goud d t the te of feet e secod. At wht te must the stig be let out whe the legth of stig ledy let out is 2 feet? movig t costt te of feet e miute, is feet fom the fiish lie whe the he wkes u 5 betwee the thid bselie d the lie of sight fom the umie to the ue. How fst iso chgig whe sechlight tht ottes so s to lwys illumite the helicote. At how my dis e secod is the sechlight ottig whe the distce betwee the helicote d sechlight is 5 feet? d the to of the cu hs dius of 2 iches, how fst is the wte level isig whe the wte is 2 iches fom the wil, the bottom is beig ushed towd the wll t the te of Vz x feet e secod. How fst is the dee? goud? (The distce s fom the bll to the goud t secods fte elese is give by s = 66?.) feet fom the fiish lie d dts off fte the totoise. Let x be the distce fom the totoise to the fiish lie d, d suose the distce y fom the he to the fiish lie is give by y = 525J x. the ue is feet fom thid bse? but 5 feet fom the light. How fst is the shdow isig log the goud whe the bll is 5 feet fom the. A kite feet bove the goud is beig blow wy fom the eso holdig its stig, i diectio 6. A bsebll dimod is sque with sides 9 feet log. uose bsebll lye is dvg fom kecod b) Who wis d by how my feet? to thid bse t the te of 2 feet e secod, d umie is stdig o home lte. Let be the gle. A sheicl blloo is iflted t the te of cubic iches e miute. How fst is the dius of the blloo t lest oe c i (,b) whee f (c) =. 2. A ldde 5 feet log les gist veticl wll. uose tht whe the bottom of the ldde is x feet. Wte is oued ito coicl e cu t the te of /2 cubic iches e secod. ifthe cu is 6 iches tll 5. The totoise d the he e hvig thei fbled footce, ech movig log stight lie. The totoise, ) How fst is the he movig whe the totoise is feet fom the fiish lie? 7. A steet light 6 feet high csts shdow o the goud fom bll tht is doed fom height of 6 feet 8. A helicote feet high is movig hoizotlly t the te of feet e secod. t flies diectly ove will give you these fomuls: hee: V=f icle: A = 2 oe: V = 22h ube: V = side 2.6.2 Review
Fid y ticl umbes of the fuctio. 9. f(x)=x6x29x. g(x)=x. k(t)=2tt 2. f(z)=zjz+ Detemie the bsolute extem of the fuctio d the xvlues i the closed itevl whee they occu.. f(x)=x25x6 [%,6J. g(x)= (,] 5. f(x)=x [,8] 6. f(x)=esc(x) [/8,%] 7. g(x)=/ [,] 8. hq=t [,5) Detemie whethe Rolle s Theoem c be lied to f o the idicted itevl. f Rolle s Theoem c be lied, fid ll vlues of c guteed by the theoem. 9. f(x) = x2 x+2 [,2) 2. f(x) = (x)(x+fl2 [,) 2. f(x)=x [,6] 22. f(x)=x [,] 2. f(x)=cosx [,2z] Aly the Me Vlue Theoem to f o the idicted itevl. ech cse, fid ll vlues of c guteed by the theoem. 2. fc)=xc2x2) [,) 25. f()=±fl [%2] 26. f(x)=x [o,i) 27. f(x)=2six+si2x [,z] 28. fg)=(x+j [,] 29. A g c cceleted fom test, tvelig 2 feet i 2 secods. Must the c hve bee tvelig t lest mh t some momet duig tht time itevl? xli. (Hit: ovet to miles d hous.)
cm t. P u 7 Th JL y( L gjq c. d <\< ( fl wt H c l_ { H9 A j_ ( _ z T ij ) * L tc l o c g + 9 M L 6 i ( T ) ) l ij fl F. (, J J+J L t D h c.d i g fl ifi o :, z(t L k > t o, c tl) D ).)..J of, f Th.,., F.G± D
t < t Go o tcp N f A, c w ( T J 9 2, F hi : t o L t.j 5 5 g i / i P s _ H > oul, ( L,:: t (Ae e vi> o t i l, ) B B.J. >>/, o (, N D fl t, cl z ) 5. s t, t ) P DAc& L, ct Lt 5 7 t
Q D, Qj ki> it 2 V fl uk, T et. 9 J s i _, kic flfl,$ oj o ( o WL.. ( L P?kjt L i\ L G d fl.i Hg Q2 t R tix tp u (N c ti, 2 (A, cft g jojct N t (A i
7 ) z L,l og 2 D\ io.7_d,,, 7 i. Mi 2 ) 9 9 t x 2 ).g H i WY 72\., V 2fl, 9 ) 7o ; L. / < fl 2 j + + i df Q bi hi, i? y?: Ø. J.. N J.Jt i f.j ( * Y $ L #9 f LJ.J s><. J f to, to 2 L, Th ( yc, F O tj ) 2 c!i i ;Lt fl 6! < fl cb l l i ti ç QJ
.) oq oin t, OQ i f z, oj oo fl s N : b}i t/ L i fa it?, l t 5 5 L) A L j J w i t fl,,. d vi bjbt9 g ( ( LA (F t), o c (P (P H L F?j J c t L ) s L o 9 Ott R l o L c L J x LñM, PD ( tj c_a t, c L c (P Z.2 2o t.,
i l \%.ç 5_) %j q ) :. $? L A ei l 7 < to?.n i P...b DT \Z x V.) 7.2 D i fl i A c. G 7Z :, 5 çq \ Ti Li _t: _!iji?. ijø. q.k i w. yl j_,,!lj v d QL ic _j cl (f) zj& t ;;j vj!? i o t, to, fl o ) R. f. N, L x l..5 i i t o e ( 2<. ¾\ 5 (7 H u jc j\ $ ( o,qq _,(, 2? qe 6 H TX? j < i N?cj 2< A ji u %J * q H l, l J\ i, j9 L 2 ( d $.. Os
LJ L fl, 9)9) +? o._ D (N t c ti 9 L ft L P g ( ft ft Li dl LsJ\ Lc J 2 l v 5 t l J. WV (, Lt L Li vi >L)J YN i & A k PD A cljl.)j ui fl 2: \i, i t j %) (_ 9 ill x 9 9) NL P : :: t_i Q i u) i Li i (A 9