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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 Xleuﬂ 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). IF 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
‘ Intw 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 WooF 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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 Fall '08
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