Mathzsltidgssfunlamwtllhenfakh: Tf g B alms an Laid & diftnttkmlaib )

,adif g

'

is , ntgrbkm laid,then

fabg'

= glbl -gl . ) .

idea : Fm the MVT,

we hnoglbtgbttjko ) ( b - a) fr se xoekih ) .

y=gk)y=jk)

of dim%

Btnaethkfthgaprttn P={ at tonic . . . ctitd. Wear write

glbtgktgltntgltn . , )tgK . ,) -gltn . a) t. . . tgltdglt , ) tgltitglt . )

And new ahgltitglti . D= gllxilltitii ) frsexieltiniti )

y=gk)y=jk)

••

My .

.

.Amaker¥,

1 ¥,

1 My'm I tfg

t , tz t} tq

t , tz +3 £4

But nw the part is tht if the swbrwkmbmteprtitmaesmll, jlxiltti - tin ) a Mlg ,Hiatt ) ltitit )

& jlxillti - tin ) amlg ,Hiatt ) ltitit )

So nw Us mhe this rigorous :

Proof: Wehw g is mtgrke

,so S!g' = Ubs' )=hf{Ulgip) : Papotkf GD } & alsofitlg't=sp{Lljip ) :

Papqtlyfg

fufe ,

if neanslwtht Lbipkglbtgkkuls:P) frallprtksp,

than it mtfllwlht

Llgltglbtgk) IUlj ).

Bt then we hwthtg '

B mtgrtk,so

Lljlttlg'), majtht both regality not be qnlitg & we he

gc4. GGI .

- UgD=Ub ' ) =)! j

so ht p={ a to < t,L

. .

.< tits be a prttm .

Then freahsknlwl Ctirti ),

the Man the fresh gates

F xieltinti ) s.it . jlxit stylist or. quirky , gltitglti D= jlxiltti - tin )

.

Now,tydefinitn mlg

'

,Hint :] ) ± gtxilt Mls : Hi . it :] ) . so

Llj # = .±f,

mlg'

,Hint :DHi - ti . i ) t Fe glxilltiti . D E ZMIG '

,Hi . itD) Hi - ti . ,) = UH

,P) .

Bt new §,

gtxiltti . to D= In lgttil -

glti.it#iJHoDHgHA.Hi)t...HgHnX-gtkDHgltntgVniD=gltntglto)=glbtgk

).

so we indeed he Lljpkglbtgkktllsip) t P,so glbtgla) = £9 '

, as desired. x#