TIP TUYN CA TH HM S 3x 2 Bi 1. Cho hm s: y = (C). x 1 Vit PT tip
tuyn ca (C) bit tip tuyn to vi Ox mt gc 450 Bi 2. Cho hm s:
y=x3-3x+7 (C). Vit PT tip tuyn ca (C) bit tip tuyn to vi ng thng
y=2x+3 mt gc 450. 2x 7 Bi 3. Cho hm s: y = (C) x +1 Vit PT tip tuyn
ca (C) bit tip tuyn to vi Ox, Oy mt tam gic cn. 3 Bi 4. Cho hm s: y
= x 3x (C) v im M ( C ) c honh x = 2 . Vit PT tip tuyn ca (C) bit
tip tuyn i qua M. Bi 5. Cho hm s: y=-x3+3x+2 (C). Tm cc im trn Ox m
t c th k c 3 tip tuyn n (C). Bi 6. Cho hm s: y=x3-6x2+9x-1 (C). T
mt im bt k trn ng thng x=2 k c bao nhiu tip tuyn n (C)? Bi 7. Cho
hm s: y=x3-3x2+2 (C). Tm trn ng thng y=-2 cc im m t k c 2 tip tuyn
vung gc vi nhau n (C). Bi 8. Cho hm s: y=f(x)=x4-x2+1 (C). Tm cc im
trn Oy sao cho t c th k c 3 tip tuyn n (C). 2x + 1 Bi 9. Cho hm s:
y = (C). Tm trn ng thng x=3 cc im m t k c tip x2 tuyn n (C). N TP
CHNG I 3 2 Bi 1. Cho hm s y=x - 3mx +2 (Cm) 1. Tm m hm s c cc i, cc
tiu. Vit phng trnh ng thng i qua 2 im cc tr ca th hm s. 2. Tm m hm
s ng bin trn (0;3) 3. Tm m hm s cho khng c cc tr 4. Tm m trn (Cm) c
2 im phn bit i xng nhau qua gc ta 5. Tm m th hm s nhn I(1;0) lm im
un 6. Tm m hm s t cc tiu ti x=2 7. Tm m th hm s ct Ox ti 3 im phn
bit 8. Tm m th hm s ct Ox ti 3 im phn bit c honh lp thnh cp s cng
9. Ty theo m, bin lun s giao im ca ng thng y=-3m+3 vi th hm s 10.
Tm m PT x3-3mx2+2=0 c nghim duy nht 11. Khi m=1: a. Kho st s bin
thin v v th (C) ca hm s b. Da vo (C) bin lun s nghim ca PT:
x3-3x2+k=0 c. Vit PT tip tuyn vi th (C) bit tip tuyn i qua B(-1;2)
d. Vit PT tip tuyn vi th (C) bit tip tuyn vung gc vi ng thng
5y-3x+4=0 e. Tm trn Ox nhng im m t c th k c ng 2 tip tuyn n th (C)
f. Tm k PT: -x3+3x2+k3-3k2=0 c 3 nghm phn bit 3 2 g. Tm k PT x 3x +
2 = k c 4 nghm phn bit h. Tm k PT x 3 x 2 + k = 0 c 3 nghim phn bit
i. Tm gi tr ln nht, nh nht ca hm s y=x3-3x2+2 trn [1;2].3
x 2 + 2mx + 2 Bi 2. Cho hm s: y = x +1 1. Tm m hm s cho: a. ng
bin trn tp xc nh ca n b. ng bin trn ( 1;+ ) c. Nghch bin trn
(-3;-2) 2. Tm m hm s cho c cc tr. Vit PT ng thng i qua 2 im cc tr
ca th hm s 3. Tm m th hm s ct Ox ti 2 im phn bit c honh m (dng) 4.
Tm m th hm s ct ng thng y=-x+2 ti 2 im phn bit m cc tip tuyn ca th
hm s ti cc im vung gc ( song song) vi nhau 5. Kho st s bin thin v v
th (C) ca hm s khi m=1 6. Chng minh rng ti mi im ca (C), tip tuyn
lun ct 2 tim cn to thnh mt tam gic c din tch khng i 7. Vit PT tip
tuyn vi th (C) bit tip tuyn i qua M(-1;2) 3 8. Vit PT tip tuyn vi
th (C) bit tip tuyn co h s gc k = 4 9. Chng minh rng trn th (C) tn
ti nhng cp im m tip tuyn ti song song 10. Tm trn th (C) nhng im A m
tip tuyn ca (C) ti A vung gc vi ng thng i qua A v I ( I l tm i xng
ca (C) ) 5 11. Tm trn th (C) 2 im M, N i xng nhau qua K 0; 2
