Cac Bai Toan Ve Ham So

[CC BI TON V HM S

***

DON XUN HUY THPT N THI-HNG YN]

MT S BI TON V HM SI.Xt tnh n iu ca hm s:

1/ Xt tnh n iu ca cc hm s sau:

;

2/ Tm cc gi tr ca tham s m hm s: a/ R ; b/ khong 3/ Tm cc gi tr ca tham s m hm s:

ng bin trn:

a/ Nghch bin trn khong (- 1; 0) ; b/ Nghch bin trn cc khong ca tp xc nh ; c/ ng bin trn khong ( -2; 2 ) . 4/ Xc nh gt ca m hs sau lun nghch bin trn R: 5/ Tm k ca a, b hs sau lun b trn R: 6/ Bit hs . n iu trn R; hi n b hay nb ? .

II.Cc tr ca hm s:A - L thuyt: Hm s y= 0 c hai nghim phn bit. Hm s (1) nu c CTR v c CTR khi PT th

1

[CC BI TON V HM SHS (2) nu c CTR th: CT l: y = (2mx+n)/q.

***

DON XUN HUY THPT N THI-HNG YN] v ptt qua C v

K th ca hs (1) ct Ox ti 3 im phn bit l : B Luyn tp:1/ Cho hs ct Ox ti 3 im phn bit . 2/ Cho hs . Xc nh m c & ct ca ths i xng qua t x 2y = 5. . Vit ptt i qua 2 ctr ca hs. Tm gt ca m ths

3/ Cho hm s: y x3 3x 2 4 . Hy tm cc gi tr ca a hai im cc tr ca hm s trn nm v hai

pha ca ng trn (C): x2 y 2 2 x 4ay a2 1 0 . 4/ Cho hm s y x3 3mx2 2m 4 (Cm).Tm m hm s c im cc i, cc tiu nm v hai pha ng phn gic gc phn t th nht. 5/ Cho hm s y x 3 3mx 2 3m 2 1x m 2 1 (Cm). Tm m (Cm) ct trc Ox ti ba im phn bit honh dng. 6/ Cho hm s y x 3 3mx 2 3m 2 1x m3 (Cm ) . Tm m (Cm) ct Ox ti 3 im phn bit trong c ng hai im c honh m. 7/ Tm gt ca m hs sau c 8/ Tm cc gt ca a v b hs 9/ Tm cc gt a,b hs 10/ Tm cc gt ca m hs2

. . . .

[CC BI TON V HM S

***

DON XUN HUY THPT N THI-HNG YN].

11/ Tm cc gt ca m hs sau c C ( CT ):

12/ (B-2007): Tm m ths sau c ctr v cc ctr cch u gc ta O:

13/ Cho hs i qua 3 im ctr ca ths. 14/ Cho hs nm trn parabn .

. Tm m hs c ctr; vit pt parabn

. Tm gt ca m hs c 3 ctr; khi hy cm c 3 ctr ca ths u

15/ Tm tt c cc gt ca m hs sau c ctr v 2 ctr tri du:

.

16/ Tm gt ca m hs sau c ctr TMK

:

.

17/ Cho hm s y thng 9 x 7 y 1 0 .

x 2 mx m 8 . Tm m hm s c cc i, cc tiu nm v hai pha ng x 1

18/ Tm cc gt ca m cc hm s sau c ctr . Tm qu tch cc ctr ca ths :2m ; x 1

a/ y 2 x 1

.

19/ (A-2005): Tm cc gt ca m hs y = mx + 1/x c ctr v k/c t CT n t/c xin bng 20/ (B-2005): Chng minh vi m bk hs sau lun c ctr v k/c gia 2 ctr ca ths lun bng3

.

[CC BI TON V HM S

***


21/ (A-2007): Tm cc gt ca m hs sau c ctr v cc ctr ca ths cng vi gc ta O to thnh tam gic vung cn ti O : .

III.Gi tr nh nht v gi tr ln nht ca hm s:1/ Tm GTNN v GTLN ca cc hs sau: ;

2/ Cho pt: 3/ Tm cc gt ca a,b hs

tm gt ca a nghim ln ca pt t GTLN . c GTLN = 5 v GTNN = - 1

4/ Tm GTNN v GTLN ca bt:

.

5/ Tm cc gt ca m : pt 6/ Tm cc gt ca m cc pt, bpt sau c nghim: ;

4

[CC BI TON V HM S7/ Bin lun theo m s nghim ca pt:

***


8/ (B-2006): Tm gt ca m pt sau c 2 nghim phn bit: 9/ Tm gt ca m bpt sau c nghim ng vi :

10/ Tm cc gt ca m : 11/ (A-2007): Tm cc gt ca m pt sau c nghim thc:

IV.S tng giao ca th hai hm s:1/ Tm cc gt ca m ths ct parabn ti 3 im phn bit .

2/ Tm cc gt ca m hpt sau c nhiu hn 2 nghim:

3/ Cho hs

; xc nh a ths ct t y = x ti 3 im pb cch u nhau . .

4/ Tm cc gt ca m ths sau ct Ox ti 4 im pbcnhau: 5/ Cho hs a/ Xc nh k ct mi ; b/ Xc nh m ct mi .

6/ Tm gt ca k t y = 2kx k ct ths sau ti 2 im pb thuc 2 nhnh ca n:

.

7/ (D-2006): Gi (d) l t i qua im A(3;20) v c hsg l m. Tm gt ca m t (d) ct ths sau ti 3 im pb: .5

[CC BI TON V HM S

***

DON XUN HUY THPT N THI-HNG YN]ti 3

8/ (D-2008): CMR mi t i qua im I(1;2) vi hsg k (k > -3) u ct ths im pb cch u nhau .

9/ (D-2009): Tm cc gt ca m t y = -1 ct ths sau ti 4 im pb c honh u nh hn 2:

10/ (A-2010): Tm cc gt ca m ths bnh phng cc honh nh hn 4 .

ct Ox ti 3 im pb c tng

11/ (B-2010): Tm cc gt ca m t y = -2x + m ct ths sau ti 2 im pb A, B sao cho tg OAB c dt bng .

V.Cc bi ton v tip tuyn ca th hm s:1/ Cho hs . M l im bt k trn (C); tip tuyn ti M ct 2

tim cn ti A v B. Gi I l g ca 2 t/c. CM: MA = MB v dt tg IAB khng i . 2/ Tm cc gt ca m ths sau t/x vi Ox: 3/ Chng minh h ng cong 4/ Cho hs . lun t/x vi nhau .

. Tm cc gt ca m ths ct t y = 1 x ti 3 im phn bit A(0;1), B,

C sao cho cc tip tuyn ca ths ti B v C vung gc vi nhau. 5/ Tm cc gt ca m ths sau t/x vi Ox ti 2 im pb: 6/ Tm cc gt ca m t 2 hs sau t/x vi nhau: 7/ Tm cc gt ca m ths sau t/x vi t y = m :6

.

[CC BI TON V HM S

***


8/ Tm cc gt ca m t 2 hs sau t/x vi nhau: 9/ (D-2005): Cho hs . M l im nm trn ths c h bng -1. Tm gt ca m

tip tuyn vi ths ti M song song vi t 5x y = 0 . 10/ (B-2006): Vit pttt ca ths bit tt vung gc vi t/c xin .

11/ (D-2007): Cho hs y = 2x/(x + 1) . Tm t im M nm trn ths bit tt ca ths ti M ct Ox, Oy ti A, B sao cho dt tg OAB bng 1/4. 12/ (B-2008): Vit pttt ca ths bit tt i qua im M( -1; -9) .

13/ (A-2009):Cho hs y = (x + 2)/(2x + 3). Vit pttt ca ths bit tt to vi 2 trc ta thnh tgvc ti O. 14/ (D-2010): ): Vit pttt ca ths bit tt vgc vi t

VI.Mt s bi ton khc:1/ Tm im c nh ca h ng cong: 2/ Chng minh vi mi m, ths cc im c nh ny thng hng . 3/ Chng minh trn ths ly bt k gt no . 4/ Tm trn ths y = (x 1)/(x + 2) cc im cch u hai t/c ca n . 5/Tm cc gt ca m t y =m x ct ths 6/ Tm trn ths ti 2 im /x nhau qua t y=x. cc im /x nhau qua im I(0; 2,5) .7

lun i qua 3 im c nh v

c 2 im khng thuc ths

d m

[CC BI TON V HM S7/ Tm trn ths

***


cc cp im /x qua t y = x 1 . qua t y = 2 .

8/ Tm pt ng cong /x vi thsx 2 4x 5 x2

9/ Cho hm s: y

(H )

Tm M thuc (H) sao cho khong cch t M n (D): 3x y 6 0 nh nht.

10/ Cho hm s: y

x 12 (C)x2

Hy xc nh hm s y = g(x) sao cho th ca n i xng vi th (C) qua A(1;1). 11/ Cho hm s y 3x 1 C . x 3

Tm mt hm s m th ca n i xng vi (C) qua ng thng (D):x + y -3 = 0.1 12/ Cho hm s: y x3 x 1 (C) v hai im A(0;1), B(3;7) trn (C). Tm M thuc cung AB ca (C) 3

sao cho din tch MAB ln nht. 13/ (A-2006): Tm cc gt ca m pt sau c 6 nghim pb: 14/(A-2008): Tm cc gt ca m gc gia 2 t/c ca ths sau bng

15/(B-2009): Vi gt no ca m th pt sau c ng 6 nghim thc pb:

---------------------- o0o ------------------8

[CC BI TON V HM S

***


9

Documents

Cac Bai Toan Ve Ham So