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Lesson_8

# Lesson_8 - 'n1 ilxbhpi`e il`ivpxtic oeayg(104010 8 lebxz...

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Unformatted text preview: 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 8 lebxz `xity qixi` :dkixr oxia xnr ,cwy inrp x"c ,ipinipa a`ei 'text :ddbd uixw di`n :dqtcd il`ivpxticd oeaygd ly miiceqid mihtynd :lex htyn f ( a ) = f ( b ) miiwzne ( a, b )-a dxifbe [ a, b ]-a dtivx f ( x ) m` . f ( c ) = 0-y jk , c ∈ ( a, b ) , c dcewp zniiw f` 1 libxz .cigie cg` iynn oexzt yi x- 1 2 sin x = 3 d`eeynly gked :oexzt .cigi iynn yxey dl yiy ze`xdl jixv . f ( x ) = x- 1 2 sin x- 3 divwpeta opeazp jxr htyn itl okle f ( π ) = π- 3 > , f (0) =- 3 < zniiwne dtivx f ( x ) :meiw • .yxey miiw miipiad ly yxey yi f ( x ) ly miyxey ipy lk oia lex htyn itl okl ,dxifb f ( x ) :zecigi • ly yxeyde ,llk zqt`zn dppi` f okle , x lkl f ( x ) = 1- 1 2 cos x > la` .zxfbpd .cigi f ( x ) 2 libxz ? p ( x ) = x 4- 6 x 3 + 24 x 2- 63 x- 2 mepiletl yi miiynn miyxey dnk :oexzt el yi dyrnly d`xp .miiynn miyxey drax` xzeid lkl el yi okle ziriax dlrnn mepilet df .miyxey ipy wx [0 , b ]-a sivx okle mepilet p ( x ) . p ( b ) > eay b > miiw , lim x →∞ p ( x ) = ∞-y oeeikn . p ( c 1 ) = 0 eay < c 1 < b miiw p (0) < < p ( b )-y xg`ne . p ( c 2 ) = 0 day c 2 < zniiwy lim x →-∞ p ( x ) = ∞-y jkn wiqp ,dnec ote`a ipy el yiy rapi f`e miyxey ipy xzeid lkl el yiy d`xp .miyxey ipy zegtl yi p ( x )-l okl .weica miyxey , p ( x ) = 4 x 3- 18 x 2 + 48 x- 63 :ly yxey yi p ( x ) ly miyxey ipy lk oia lex htyn i"tr 1 , p 00 ( x ) = 12 x 2- 36 x + 48 :ly yxey yi p ( x ) ly miyxey ipy lk oia ,lex htyn itl aeye ( Δ = b 2- 4 ac = 36 2- 4 · 12 · 48 < ik) miiynn miyxey el oi`y ireaix mepilet df la` ipy xzeid lkl yi p ( x )-ly o`kne cg` iynn yxey xzeid lkl yi p ( x )-ly `id dpwqnd .miiynn miyxey ipy weica yi p ( x ) mepiletl k"dqa .miiynn miyxey (onf yi m`) 3 libxz . (0 , 1) rhwa yxey yi g ( x ) = 4 ax 3 + 3 bx 2 + 2 cx- ( a + b + c ) `ad mepiletl ik gked :oexzt . G (0) = G (1) = 0 oke G ( x ) = g ( x ) zniiwn G ( x ) = ax 4 + bx 3 + cx 2- ( a + b + c ) x divwpetd . (0 , 1)-a yxey yi G ( x ) = g ( x ) zxfbpl ,lex htyn itl :'bpxbl htyn-y jk c ∈ ( a, b ) zniiw f` ( a, b )-a dxifbe [ a, b ]-a dtivx f ( x ) m` f ( c ) = f ( b )- f ( a ) b- a ....
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Lesson_8 - 'n1 ilxbhpi`e il`ivpxtic oeayg(104010 8 lebxz...

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