KHO ST S BiN THIN V V TH HM S A THCCC BC KHO ST HM S y= ax3+bx2+cx+dHM S TRNG PHNG y= ax4+bx2+cLuyn thi i hc online | n thi i hc 2014-2015

xyOLm th no c c th nhth ny ??

1.Cc bc kho st s bin thin v v th hm sTm tp xc nh . Xt s bin thin ca hm s a) Tm gii hn ti v cc v gii hn v cc ( nu c ) ca hm s . Tm cc ng tim cn ca th ( nu c )b) Lp bng bin thin ca hm s , bao gm :Tm o hm , xt du o hm , xt chiu bin thin v tm cc tr ca hm s ( nu c ) , in cc kt qu vo bng .3. V th hm s V cc ng tim cn ca th hm s Xc nh mt s im c bit ca th nh giao im vi hai trc .Nhn xt th : ch ra tm i xng ( nu c , khng chng minh )

2. Hm s y= ax3+bx2+cx+d ( a0)VD1. Kho st s bin thin v v th hm s y= x3- 3x +2Gii1. Tp xc nh RTm tp xc nh . Xt s bin thin ca hm s 2.S bin thin ca hm s a) Tm gii hn ti v cc v gii hn v cc ( nu c ) ca hm s . Tm cc ng tim cn ca th ( nu c )b) Lp bng bin thin ca hm s , bao gm :Tm o hm , xt du o hm , xt chiu bin thin v tm cc tr ca hm s ( nu c ) , in cc kt qu vo bng 3. V th hm s a) Gii hn ca hm s ti v cc Luyn thi i hc online | n thi i hc 2014-2015

b) Bng bin thin y/ = 3x2-3y/= 0 3x2 -3 = 0 x =1 hoc x =-1xy/y-+-1100+-+-+40Hm s ng bin trn cc khong ( -;-1) v (1;+) , nghch bin trn khong ( -1 ;1)Hm s t cc i ti im x =-1 , gi tr cc i y =4 .Hm s t cc tiu ti im x =1 , gi tr cc i y = 0 .

3. th Giao im th vi Oy l ( 0;2)Giao im th vi Oxy= 0 x3-3x+2 = 0 x = 1 hoc x =-2 th nhn im U(0;2) lm im un

im un ca th hm sy = x3-3x +2y/ =3x2 -3y// =6xy// = 0 x = 0U(0;2)Uim U ngn cch phn li v phn lm c gi l im un ca th hm s .?Vy lm th no tm c im un U ?

Bng du y//xy//-+00-+Nu hm s y= f(x) c o hm cp hai trn mt khong cha im x0 , f//(x0) =0 v f// i du khi x qua x0 th U(x0;f(x0)) l mt im un ca th hm s y= f(x)Ta thy y// i du khi x qua x= 0 nn th hm s c im un U(0;2)Luyn thi i hc online | n thi i hc 2014-2015

VD2.Kho st s bin thin v v th hm s y= -x3+ x2 +x

3.Hm s trng phng y= ax4+bx2+c ( a 0)VD3. Kho st s bin thin v v th hm s y= x4 -2x2 -2Gii 1/ Tp xc nh R2/ S bin thin ca hm s a) Gii hn ti v cc b) Bng bin thiny/= 4x3 4x = 4x(x2 -1)y/ = 0 4x(x2 -1) = 0 x = 0 hoc x = 1 hoc x =-1

xyy/0-11-000+-+--2-3-3++Hm s nghch bin trn cc khong ( - ;-1) v (0;1) , ng bin trn cc khong (-1;0) v (1;+ )

Hm s t cc i ti im x = 0; gi tr cc i y= -2 .Hm s y cc tiu ti im x = -1 hoc x =1 , gi tr cc tiu y =-33/ th im un Ta c y// = 12x2 -4xy//-+00+-+Ta thy y// i du khi x qua x = nn th hm s c hai im un Luyn thi i hc online | n thi i hc 2014-2015

Giao im ca th vi trc tung (0;-2) Ga tr c bit x= -2 => y=6x= 2=> y=6-20xy2-26

VD 4 .Kho st s bin thin v v th hm s y= -x4 +2x2 +22xy0Luyn thi i hc online | n thi i hc 2014-2015

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