Page 27 - Math Grade 12 (Advance)

PROEUS DARA

2.

c.')) 0 c::t, ~ C) 0 I r 0 C:::.
mG~SI:H'l m sb M tf::lrnmmgLf:lU XE I ' m~f'(x)~M &Sl8Till.5U~StHi

a, bE I tf::lrn a<b tf:'iQIS m(b-a)~f(b)-f(a)~M(b a) '1

I cJ cf C:, C)) C::.
g'(x) = f'(x)-m tf:'iQIS g'(x):2:0 L?'iU XE I '1 'i:flSSt15Gl g(x) dlH~f:'i'eS&nS&rn I sb
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tnstrn
"" [a, b] tf:'iQIS g(b)-g(a):2:0 y_ [f(b)-mb]-[f(a)-ma]:2:0t4_
m(b-a)~f(b)-f(a) (1) ~G~tf::li tf:l2jH~f:'i'eS h: x '-7 f(x)-Mx 'i:flStf::l1t~nli

l sb h'(x) = f'(x)- M '1

tf:'iQIS h(b)- h(a) ~ 0 t4_ [f(b)- Mb]- [f(a)- Ma] ~ 0 t4_ f(b)- f(a) ~ M(b- a) (2) '1

m-e (1) sb (2) tf:'i9lmms tti f dlHS?'i'eS'i:flStt:l1t~trn [ tf::lbli~RU XE [ '
--.:> 1 L.
m~f'(x)~M r;mgtf:lQIS m(b a)~f(b)-f(a)~M(b-a) '1

ttl rn f(x) = JI+x '1

[ 1] 1 1
0
'
2. uqpnmGr;mgTilu xE o, t?'iQIS 1 + J6x ~ f(x) ~ 1 + 2x '1
'
2
rufiw :
011
n. r'hlll~fit~H-ets f'(x) thmgLf:lli xE [o, ~]
tf:l'i:fls J<x) = JI+x tf:lms f'<x) = ~ !'CO):::: f'<x):::: 1{D
2
,
nn ru f'(O) = ~ , rG) = ~

~msg tJtmgTilti xE [o, ~] tf:'iQIS ~~f'(x)~~ '1
2. t?'i'HlS xE[o, ~], ~~f'(x)~~

"'"il 0 ... 0 ' 1 1
H ~ ~ ~ S-. t\5'e.ffH1 nt rtfl S'i:flS n rul fi tf:'iQIS J6 (x- 0) '.5 f(x)- f(O) ~ 2(x- 0)

n:nru j(O) = 1 ~msg I+ ~x~f(x)~ 1 +~x '1

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