ung dung dao ham.pdf

4/4/2015 HongNgcTh:BigingI.4GTLNGTNN(TrnTrungKin)

http://hoangngocthe.blogspot.com/2012/09/baigiangi4gtlngtnntrantrungkien.html 1/11

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HongNgcThChlnthtm

Dnhchohcsinh Dnhchogiovin Th Knim Hihc vui Khoahc thiHSG ngdngton

NHN:CHUYNLTH

Bi ging I.4 GTLN GTNN (Trn TrungKin)

THHONGNGC THURSDAY,SEPTEMBER27,2012

BigingnythucKhanthiH2013.Tholunvtcuhitiy

XembigingI.1I.2I.3

ThngbovlchhcngklmGingvinngklmhcvin

Liniu

Phngphpsdngtnhniucahmstrongccbitonchngminhbtng thc (BT) c l tr thnh mt trong nhngphng php kinh in,chnhvthbnccthtmthyphngphpnytrongttcccquynschvBT.Tuynhin,tronghuhtccquynschvitvBTnichungvphngphpsdngtnhniucahmsniringchmidnglivicnuramtBTvchngminh,mkhngnitulicBT.Trongchuynny ccBTcnglnhngBTquenthuc vucchngminhbngphngphpsdngtnhniucahms,tuynhinvntrngtmyltccBTtacthsngtoraccBTkhc.Hyvngrngqua,hcsinhcthbitquylvquenkhingtrcmtBTly cng lphngphpquantrngthngxut hin trong cc k thi tuynsinhihccaongtrongnhngnmgny.

Bitonchung:ChngminhBTCchgii:

ChuynBT thnh:TmTXcahms ,gislTnh vgiiphngtrnh ,suyranghim.Lpbngbinthin BTcnchngminh.

Ch:

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Hcgiichachcthnhcng,thnhcngchachchnhphc.

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thiTSHmntonkhiBnm2014

TbitonthiChnituynDaklak

thiOlympic30/4lp11nm2012

PHNHIMI

AnhThanhqukhen.:DThHongNgc

pnl534qu...TUANHUYNHTHANH

Xinli,titnhtonnhm1cht.Lpluncab...ThHongNgc

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thtaphidavo tpxcnhca tmtpgi trca ,txthmsmicnl .TrongmtsbitontacthpdngccBTCsi,Bunhiacopski,saumixthms.

ReadMore

MTSVDTMGTLN,GTNNCAHMSTrongmcnytitrnhbymtsvdtmGTLN,GTNNcahms

VdI.1:TmGTLN,GTNNcahms .Gii.TX:

Lp bng bin thin ta thy:

VdI.2:TmGTNNcaiukin:

Tiy,chcnbnhphng2vln,vtiukin lxong.

Cnghaivca(2)tac$$\left\{{\begin{array}{*{20}{c}}{x\geq2\veex\leq\frac{3}{2}}\\{\frac{{25}}{{{x^2}+4x+21}}=\frac{{49}}{{4{x^2}+12x+40}}}\end{array}}\right.$$

Nghim bloi

Vy

VdI.3:Chngminhrng:

Gii.

BT

Xthms c

Bitp:

PLUS.MATHS.ORG

Sexualstatistics:Thepodcast

Sexualstatistics

TRANGCHDINNTONHC

TiliuhnhnthiH4/3/2015

TONHCGOOGLETINTC

GiodcVitNamcthxasTon,L,Hakhng?VTC

MATHEMATICSGOOGLETINTC

ThemathematicsoflifesavingregulationTheHill(blog)

VanGaalpointstomathematicsofUnited'stitlehopeHere'swhatit...NBCSports.com

SCIENCEDAILY:MATHEMATICSNEWS

Mathematician's2015MajorLeagueBaseballprojections

VNMATH.COM|PNTHIIHCTONLHASINHANHNM2011KHIABCD

GiicccukhtrongminhhathiTHPT2015bngnhiucch

TONHCVITNAM|TONTRUNGHC|TONIHC

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VNcnnxinnbaogi?

ZETAMU

TrchiDobble:mtthihsgtonPhp2015

STAYTHCHHCTON

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VUHAVAN'SBLOG

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DAMTHANHSON'SBLOG

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I.1.TmGTNN,GTLNcahms

I.2.TmGTNN,GTLNcahms vi

I.3.TmGTNN,GTLNcahms

I.4.TmGTNN,GTLNcahms vi

I.5.TmGTNN,GTLNcahms .

II.KTHUTGIMBINTRONGTMGTLN,GTNNCABIUTHC.1.KthuttmGTLN,GTNNbngphngphpth

V d II.1.1: Cho tha . Tm gi tr nh nht ca biu thc.

Gii.

Tgithittac .Khi .

Xthms .

Tac:

Tbngbinthintac ,tckhi .

Nhnxt:Bitonnycgiibngcchthmtbinquamtbincnliriavkhosthms

V d II.1.2: Cho tha . Tm GTNN ca biu thc.

Gii.Tgithittac .khi=""k="\frac{x}{{\sqrt"vi=""t=""l=""i=""th=""nh=""1=""=""x=""frac=""sqrt=""span="">

Xthms .

Tac:

Vy tckhi .

Nhnxt:Bitonnycgiibngcchthmtbinquamtbincnlivsdngccgi thitnhgi bincnli.T tmcgi trnhnhtca hmschamtbinb chn.Ngoiratac thdngBTCsi,Bernouli,Jensen,chngminhBTny.2.CckthutdnbinVdII.2.1:(khiB2007)Choccsthckhngmthamn .Tmgitrnhnhtcabiuthc:

t

Xthmsohm

Davobngbinthin,tac

ngthcxyrakhi hayhonvcab

Sngbaydcbin

NGUYNHUINH

DYHCTCPHMTRUYNTHEOCTRNGTHIPHPLOITH

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TitrnWordpress

Nghthutgiiquytvn

Khohctrctuynvchclngt

LMINHAN

[ThithH]HHKG

STORE

Tmhthctruyhiviukinutnhsxunhphndinbitlunchahaibt1lintip.

MATHEMATICS...

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JULIEL'SBLOG

NumberTheory

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VdII.2.2:(thiHkhiBnm2011)Cho l2sthcdngtha .TmGTNNcabiuthc

Ta c:

TheoBTCauchytac

t

Khosthmstrntac:

VdII.2.3:(dbkhiDnm2008)Chosnguyn v2sthckhngm .Chngminhrng

Dubngxyrakhino??

Xt ,tac:

Xt

Tachngminh:

Tac:

Khngmttnhtngqut,gis .t

Khi , bt ng thc cn chng minh tng ng vi:

Xthms:Tac:Suyra gimtrn

Vyvi th:ngthcxyrakhi ..

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VdII.2.4:Cho l3sthcthuc .Tmgitrlnnhtcabiuthc:

t .Xemylhmtheobin ,cnb,clhngs.

Tac:

Nu v , suy ra:tngtrn

Xem lhmtheobin .Khi:

Do gimtrn ,suyra .

Xem lhmtheobin .Khi:

Lpbngbinthinca trn ,tac: .

*Nu v .Tktqutrntac .

Mtkhc:

Vy

VdII.2.5:Cho lbasthcthucon v .Tmgitrnhnhtcabiuthc

t:tKhi vTacXtbitonminycccbin v bnhngnntadonngthcxyrakhi

Khi vi

Sosnh vi tadonc tgitrnhnhtkhiKhi vtatmcccgitrca tngngl

V d II.2.6: Cho tha mn . Chng minh

Ta c:

t:Tac:Dthy: lmthmbcnhtvibin .Talic

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#

#

#

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0 0

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Suyra: .iuphichngminh.

Dubngxyrakhi: .

VdII.2.7:Cho thomnlccsthc:

.Tmgitrlnnht,nhnhtcabiuthc

Tgithitsuyra:

ttac

.

Mtkhc

nn

.t

bitontrthnhtmGTLN,GTNNca:

Tnh

Dohmslintctrn

nnsosnhgitrca

choraktqu:

,

VdII.2.8:(KhiA2012)Choccsthc thamn .Tmgitr

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nhnhtcabiuthc:

Cch1:T gi thit ta c (1) trong 3 s lun c 2 s cng du,khngmttnhtngqutgishaisl tacThay vo tac

t xt

Nnsuyrahm ngbintrn nnTac: vyDubngxyrakhivchkhi

Cch2TachngminhXthmC v .Vy(*)ngpdng(*),tac:

pdngbtngthc: tac:

Do:

M suyraSuyraKhi thdubngxyra,vygitrnhnhtca bng3.

V d II.2.9: (Khi B2012) Cho cc s thc tha mn v.TmGTLNcabiuthc

Tac vythtac vbiuthccvitlithnh

Hayl

Bygitachrng

TytacBiuthcvitlil

]45]

]56]

]64]

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Kho st hm s ny ta c du ng thc xy ra khi

V d II.2.10:Cho l cc s thc khng m,khc nhau tng i mt tha mn.Chngminhrng:

Khng mt tnh tng qut gi s khi ta c

Khitachcnchngminh:

Mlic:

Vthtasichngminh:

Tac:

$$f'(t)=\frac{{1}}{{{{(t2)}^2}}}+1f'(t)=0\Leftrightarrowt=3\minf(t)=f(3)=4$.$Vybitongiiquytxong.

VdII.2.11:Cho thcdngtha .Tmgitrnhnhtcabiuthc

Vi ,tacVi ,tatKhi:

Tac

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)4

4 5 6

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0

4 5 4

5

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5

5

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5

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Lpbngbinthinrisuyraktqusau:

,tckhivchkhi hoc

,tckhivchkhi hoc

Bitpngh

Bi1: (B2009)Cho cc s thc thay i v tho mn TmGTNNcabiuthc

Bi2:(B2006)Cho lccsthcdngkhngi.TmGTNNcabiuthc:

Bi3:Ccsthckhngm thomn: TmGTLNcabiuthc

Bi4:Cho 0v .Chngminh

Bi5:(DbkhiA)Cho 0thamn .Chngminh

Bi 6: Tm gi tr ln nht v nh nht ca hm strnon

Bi 7: (Khi A 2009) Cho l cc s thc dng tha mn.Chngminhrng

Bi8:(dbTSH2003khiB)Tmgitrlnnht,nhnhtca

trnon

Bi9:Cho .TmMax,MincaA= .

Bivitlinquan:BigingI.2Cctrcahms(Phn1)BiI.1TnhniucahmsTmiukincathams hms niuBigingI.7BitonkhongcchBigingI.6BitontiptuynBigingI.5ngdngcaohmBiI.3StnggiaocaccthBigingI.2Cctrcahms(phn2)

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