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BI TON LIN QUAN N KHO ST HM SNH L VI T

Phng trnh bc 2: ax2+bx+c=0 (a 0)

X1+ x2=a

b; x1x2=

a

c;

axx

= 21

Phng trnh bc 3: ax3+bx2+cx+d=0

X1+ x2+ x3=a

b; x1x2x3=

a

d; x1x2+x2x3+x3x1=

a

c

CC BI TON V NG BIN

NGHCH BIN

Cho hm s ( )xfy = c tp xc nh l min D.f(x) ng bin trn D ( ) Dxxf ,0' .f(x) nghch bin trn D ( ) Dxxf ,0' .(ch xt trng hp f(x) = 0 ti mt s hu hn im trn min D)

Thng dng cc kin thc v xt du tam thc bc hai:

f(x)=ax2+bx+c

1. Nu 0 < th f(x) lun cng du vi a.

2. Nu 0 = th f(x) c nghim 2b

x a= v f(x) lun cng du vi a khi 2b

x a .3. Nu 0 > th f(x) c hai nghim, trong khong 2 nghim f(x) tri du vi a, ngoi khong 2 nghim f(x) cng du vi a.

So snh nghim ca tam thc vi s 0

* 1 20

0 0

0

x x P

S

>

< < >

< < > >

* 1 20 0x x P < < >

.

hm s ( )y f x= c hai cc tr nm pha di trc honh 0. 0C CT

C CT

y yy y

+ .

hm s ( )y f x= c cc tr tip xc vi trc honh . 0C CT y y = .

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x1

2

0)(0

S

a f hoc >

2

0)(0

S

a f

HM S BC 3

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Hm s y = f(x) =ax3 + bx2 + cx+ d, vi (a 0)Min xc nh: D= R

o hm: y=3ax2 +2bx+c, y=6ax +2b-Nu y c hai nghim phn bit th hm s c 2 cc tr-Nu y c nghim kp hm s n iu trn min xc nhMt s tnh cht

Tnh cht 1: Hm s ng bin trn R

>

0

0

a

Tnh cht 2: Hm s nghch bin trn R

0Tnh cht 4: th nhn im un lm tm i xng. (Di tm i xng v gc ta , thy ym l hm s l )

Theo cng thc di trc

+=

+=

yYy

xXx

Thay x, y vo phng trnh hm s ta cY+yo=a(X+xo)3+ b(X+xo)2+c(X+xo)+d (1) Y=aX3+g(xo)X L hm s lTnh cht 5:(Bi ton 1) Tip tuyn ( h s gc ) max hay minTa phi da vo phng trnh y thao tc

y=3ax2 +2bx+c

B1: Rt 3a ra ngoi k=y=3a(xo+a

b

3)2 +

a

bac

3

2^3

B2: a>0, th kmin =a

bac

3

2^3 Khi xo=-

a

b

3

a

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- Nu (1) c nghim x0 th (1) (x-xo)(ax2+b1x+c1)=0b, Xc nh iu kin ca tham s phng trnh c k no phn bit

-on n0 x1 :(x-xo)(ax2+b1x+c1)=0

=++=

=

011)(2 cxba xxg

x ox

+ Mt nghim duy nht:

=

=

0)(

0

x og

g

+ Hai nghim phn bit:

=

0)(

0

x og

g

hoc

=

>

0)(

0

x og

g

-Khc

+ Mt nghim Ct 0x ti 1 im

>0* yCTyCD

euHmsodondi

>

>

0*

0'

0'

y C y C D

y

y

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+Hai nghim ( C)ct 0x ti hai im

=

=

0)2(*)1(

b i p h nn g h i . m2C 0'

xyxy

y

+ba nghim phn bit (C ) ct 0x ti 3 im phn bit

Hm s c cc i cc tiu v yCD*yCT

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Tnh cht1: Hm s c cc tr vi mi gi tr ca tham s khi a 0Tnh cht2: Hm s c cc i v cc tiu

y=0 c 3 nghim phn 02