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4.7 Theorems - M L 4.7 Theorems abou Continuous A £9...

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Unformatted text preview: M. L- 4.7 Theorems abou+ Continuous A £9 DIF‘FcYenTlablO Fund/ans ! g 5 g 3 ' o iflecal! I p.% H COHTIHUOMS {in has aymph +ha+can be, drawn 14»va m:th +he penal fiom mpapac j Pm; A» {immon f is dtPFcrenTIable 19V my X-leufl whe h Hx+h - ._ ‘ 1 ’5 Mme 3‘ H") .. f’{x) exMS. i p.97 14‘— HY) ‘25 diffirennable 62+ a. palm x=aJ than Ha) is can-(mucus 51+ 15:61.. 4 a. global ma)c 80 CL global mm on [4329]. g "'4" and has at local max or mm M x=C (#me [5 nm‘ on eIMpwht. If f is dWQrmmb’ i Lam Suppose f ls defined on an m'tewal [4pr i (11‘ F0, men 3%):0, % ‘ i 7 IF 43 Continuous on [(1qu than fhas ; FA..- Warm... ; 31h .. Tm ‘Meanv VditE-‘Thm IF f Continuous on Cam and diffirennabk ‘ on (GM, than mere eers (.1. number 5) wtfh a<c¢b SUCh {.70 3, 'Fld) b -— a. (Bee disasslm é: plci'Ure on p.803) ( I iThm‘hll The Increas‘tg Fen Thm , p.302 ‘3 SUppose Thai 3‘: LS continuous/on [Cub] and leevennable an (ab)- 1. 11“ 300070 on (a b) then mamas: I 3 f on [0%] a\ 110 {WV/0 0n (cub) , then f is mondecreasmg on [cub] J 1 Thumb The Consmm Fm Thnv p.309 suppose f is continuous on Kalb] and dammmgable on (01b). I-F f’kao or) (am) finen f is Consfam- on Cmbl 1 t J W~Afi ._ w ._..,__.___ A l Pa” The Raccfimcg Ramada i 3 Suppose 3 A: h an commuous on i itabe & dIFFerenTtabla on (0)33“) & WWW“! WW" 3’60 s. h’(x) fir add: , i ‘1? gins—Ma) finer) gméhlfl 7%,:st } . 1:9- 3(b)==*h{b) W 9602 W) Wags!» Than 0F 9m 89 hlx) as posmms 019/2. 1 horses on a. mamm. 1 1 J Horse hm alums moves fisflr Wm 900. ‘W 1 i If» My Smyf Weaker, horse W) ‘3 always ahmd. ' i ‘ Int-w W3 “EWSh WW) Mm 90¢) ! was ahead durum wholo race. Examgle. \ A Use. Raccmck Wmapie +0 Show W i e" 7/ 1+5: firm! 35- Woo-F N/X) ; - -V , / Call 300v- H’X . x Can hm = 6* n01? 9'(x‘)::] amt h‘(X)=€X We, knew firom p WM '71-:- 3’t’x) fir an an: Observc mat? 9(0)=-h(o)=l so #765 g *S‘taY‘l' 'l'OfiEThEY‘ all Oéxvéws‘wc =$O Knaw' flmrf hIx) 7/30). w ' Now", when X<O ) we, can see onpmph W1” W00 5 3‘00 ‘H/nn’gs have {40 prped. .. Com} 6mm ~m4xso WW 0%» b=0 and 30 9mg Mx) 1 fir all x50. , Thus) l+x sex V76 ...
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