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Vcpkj Lmskj Monhlrm Jokja
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Tcoyecbkmo Me hxprhsskce ke thrb ci scbh vmrkmloh(s) ks jmoohf m pcoyecbkmo. pcoyecbkmo. Icr hxmbpoh i(x) 2
htj. mrh ect
pcoye oyecbkmos. os. V`us, m rmtkcemo x kethn thnrmo iuejtkc tkce ci ‐x‛ i ‐x‛ ks smkf tc lh m pcoyecbkmo, ki t`h pcwhrs ci ‐x‛ i ‐x‛ ke t`h thr thrbs ci t`h pcoyecbkmo mrh ehkt`hr irm irmjtkces ecr ehnmtkvh kvh. V`u V`us, me hxprhsskce ci t`h icrb
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e ‚= ‚= + … + m x + m ks jmoohf m pcoyecbkmo ke vmrkmloh x w`hrh e i(x) 2 me xe + me ‚= ‚=x o 4 lh m pcsktkvh kethnhr mef m4, mo, ...,me lh jces jcestm tmet ets s (rhm (rhmoo eubl eublhr hrs) s)..
Fhnrhh ci m Tcoyecbkmo V`h hxpcehet ci t`h `kn`hst fhnrhh thrb ke m pcoyecbkmo ks aecwe ms kts fhnrhh. Icr hxmbpoh i(x) 2 6x-:/< ks m pcoyecbkmo pcoyecbkmo ke t`h vmrkmloh vmrkmloh x ci fhnrhh fhnrhh =. p(u) 2 :u: + u< + 8u ‚ 9 ks m pcoyecbkmo ke t`h vmrkmloh u ci fhnrhh :. q(t) 2 8 ks m pcoyecbkmo ci fhnrhh zhrc mef ks jmoohf m jcestmet pcoyecbkmo. Okehmr Tcoyecbkmo M pcoyecbkmo ci fhnrhh ceh ks jmoohf m okehmr pcoyecbkmos. Ke nhehrmo i(x) 2 mx + l, w`hrh m ≤ 4 ks m okehmr pcoyecbkmo.
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Icr hxmbpoh i(x) 2 :x ‚ :x ‚ > ks m lkecbkmo ms kt jcetmkes twc thrbs. n(y) 2 0y ks m bcecbkmo ms kt jcetmkes ceoy ceh thrbs. ]umfrmtkj Tcoyecbkmos M pcoyecbkmo ci fhnrhh twc ks jmoohf m qumfrmtkj pcoyecbkmos. Ke nhehrmo i(x) 2 mx< + lx + j, w`hrh m ≤ 4 ks m qum qumfrmt frmtkj kj pcoy pcoye ecbkmo bkmo.. Icr hxmbpoh i(x) 2 x< ‚ >x + 0 ks m trkecbkmo ms kt jcetmkes : thrbs n(y) 2 8x< ‚
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Lkqumf Lkq umfrmt rmtkj kj Tco Tcoyec yecbkm bkmoo M icurt` fhnrhh pcoyecbkmo ks jmoohf m lkqumfrmtkj pcoyecbkmo ke nhehrmo. i(x) 2 mx6 + lx: + jx< + fx + h, m ≤ 4 ks m lk qumfrmtkj pcoyecbkmo. Whrc ci m Tcoyecbkmo M rhmo eublhr m ks m zhrc (cr rcct) ci m pcoyecbkmo pcoyecbkmo i(x), ki i (m) 2 4 Icr hxmbpoh Ki x 2 = ks m rcct ci t`h pcoyecbkmo :x: ‚
M pcoy pcoyec ecbk bkmo mo ci fhnr fhnrhh hh e `ms `ms e rcc rccts ts..
(<)
M okehmr pcoyecbkmo ci i(x) 2 mx + l, m ≤ 4 `ms m uekquh rcct nkvhe ly x 2 -l/m
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(:) Hvhry rhmo rhmo eublh eublhrr ks m rcct rcct ci t`h zhrc zhrc pcoyec pcoyecbkmo. bkmo. (6) M ece-zhrc jcestmet jcestmet pcoyecbkmo pcoyecbkmo `ms ec rcct. \hbmkefhr V`hcrhb Oht i(x) lh m pcoyecbkmo ci m fhnrhh nrhmthr t`me cr hqumo tc ceh mef m lh mey rhmo eublhr, ki i(x) ks fkvkskloh ly (x ‚ m), t`he t`h rhbmkefhr ks hqumo tc i(m). Hxmbpoh =7 Ikef t`h rhbmkefhr w`he i(x) 2 x + =4 ks fkvkfhf ly x ‚ <. Zcoutkce. ^`he i(x)ks fkvkfhf ly x ‚ x ‚ <, t`he rhbmkefhr ks nkvhe ly i(<) 2 <(<): ‚ =:(<)< + =>(<) + =4 2 =9 ‚ =9 ‚ 8< + :6 + =4 2 0 V`us, ce fkvkfken i(x) 2 << ‚ << ‚ =:x< + =>x + =4 ly x ‚ x ‚ <, wh nht t`h rhbmkefhr 0.
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Imjtcr V`hcrhb Oht i(x) lh m pcoyecbkmo ci fhnrhh nrhmthr t`me cr hqumo tc ceh mef m lh mey rhmo eublhr suj` t`mt i(m) 2 4, t`he (x ‚ m) ks m imjtcr ci i(x). Jcevhrshoy, ki (x ‚ (x ‚ m) ks m imjtcr ci i(x), i (x), t`he i(m) 2 4. Hxmbpoh <7 Z`cw t`mt x + < ks k s m imjtcr ci t`h pcoyncemo x < + 6x + 6. Zcoutkce. Zcoutkce. Oht i(x) 2 x< + 6x + 6 (x + <) 2 {x ‚ {x ‚ ( ‚<)} ‚<)} ks m imjtcr ci i(x) ki i( ‚<) ‚<) 2 4 Ecw, i( ‚<) ‚<) 2 ( ‚<) ‚<)< + 6( ‚<) ‚<) + 6 2 6 ‚ 6 ‚ 0 + 6 2 4 @hejh, x + <, ks m imjtcr ci i(x). Xshiuo Icrbuomh
(k)
(x + y)< 2 x< + y< +
( k k)
(x ‚ y)< 2 x< + y< ‚
(kkk)
(x< ‚ y<) 2 (x + y) (x ‚ (x ‚ y)
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(kv)
(x + y): 2 x: + y: + :xy(x + y)
(v)
(x ‚ (x ‚ y): 2 x: ‚ y: ‚ :xy(x ‚ :xy(x ‚ y)
( vk)
(x: + y:) 2 (x + y) (x< + y< ‚ xy)
(vkk)
(x: ‚ y:) 2 (x ‚ (x ‚ y) (x< + y< + xy)
(vkkk)
(x + y + z)< 2 x< + y< + z< + <(xy + yz + zx)
(kx)
(x: + y: + z: ‚ :xyz) 2 (x + y + z) (x< + y< + z< ‚ xy xy ‚ ‚ yz yz ‚ ‚ zx)
(x)
Ki x + y + z 2 4, t`he x: + y: + z: 2 :xyz
Mosc, (k)
(xe ‚ me ) ks fkvkskloh ly (x ‚ (x ‚ m) icr moo vmouhs ci e.
(kk)
(xe + me ) ks fkvkskloh ly (x + m) ceoy w`he e ks cff.
(kkk)
(xe ‚ me ) ks fkvkskloh ly (x + m) ceoy icr hvhe vmouhs ci e.
(kv)
(xe + me) ks ehvhr fkvkskloh ly (x ‚ (x ‚ m).
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Hxmbpoh : 7 Imjtcrksh <=9x: ‚ =<8y: Zcoutkce. Zcoutkce. <=9x: ‚ =<8y: 2 (9x): ‚ (8y): Qusken x: ‚ y: 2 (x ‚ (x ‚ y) (x< +y< + xy)R 2 (9x ‚ (9x ‚ 8y) Q(9x)< + (8y)< + (9x) (8y)R 2 (9x ‚ (9x ‚ 8y) (:9x< + <8y< + :4xy) Hxmbpoh 67 Zcoutkce.
Fkvkfh ‚ =6x< ‚ =:x + =< ly
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Bmxkbub mef Bkekbub Ymouh ci m Tcoyecbkmo Oht i(x) lh m pcoyecbkmo. V`he, i(x) `ms ocjmooy bmxkbm ci bkekbm vmouhs mt m, ki i(m) 2 4. Ki i(m) 5 4, t`he i(x) `ms bkekbub vmouh mt x 2 m. Ki i(m)? 4, t`he i(x) `ms bmxkbub vmouh mt x 2 m. Hxmbpoh 87 ^`kj` ci t`h icoocwken ks ect e ct m pcoyecbkmo3 (m) 8x< ‚ 6x + = (j) x ‚ < /8 /8 Zcoutkce. ( m) 8x< ‚ 6x + = ks m qumfrmtkj pcoyecbkmo ke ceh vmrkmloh. ( l)
ks ect m pcoyecbkmo ms kt fchs ect jcetmke me kethnrmo pcwhr ci x.
(j) pcwhr ci x
ks ec ect m pc pcoyecbkmo ms ms kt kt fc fchs ec ect jc jcetmke me me ke kethnrmo
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Luy JZMV Tmphr -< Ztufy Akt ke @mrf Jcpy7 `ttp7//kmshxmbpcrtmo.jcb/jkvkoshrvkjhs/stufy-akt/kms-prh/jsmt-pmphr-< Jokja @hrh tc Gcke Ceokeh Jcmj`ken icr JZMV Tmphr -<7 `ttp7//kmshxmbpcrtmo.jcb/jkvkoshrvkjhs/jcurshs/kms-prh/jsmt-pmphr-<
