chuyên đề khảo sát hàm số 12

  !"#$%&'((()$%( *+,-.,       !  ( ) ( )  1 1 ' . ' . . '           - - = =a  ( ) ( )  1 ' ' ' 2 2      = =a   ' ' 2 2 1 1 1 '     æö æö ÷ ÷ ç ç = - = - ÷ ÷ ç ç ÷ ÷ ç ç è ø è ø a  ( ) ( ) ' ' '.         = =a  ( ) ( ) ' .ln ' '. .ln           = =a  ( ) . ' '. '.    = +  ' 2 '. '       æö - ÷ ç ÷ = ç ÷ ç ÷ ç è ø  ( ) ( ) sin ' cos sin ' '.cos    = =a  (cos )' sin (cos )' '.sin    = - = -a  ( ) ( )  2 2 1 ' tan ' tan ' cos cos      = =a  ( ) ( ) 2 2 1 ' cot ' cot ' sin sin      = - = -a  ( ) ( )  1 ' ln ' ln '      = =a  ( ) ( )  1 ' ln ' ln '      = =a  ( ) ( ) 1 ' log ' log ' ln ln          = =a " #$% &'()*+,-.*/01 2.'()*(3245(3065(708*  2 2 sin cos 1 + =  tan .cot 1  = sin tan cos    =  cos cot sin    =  2 2 1 1 tan    + =  2 2 1 1 cot sin   + = sin2 2sin .cos  = 2 2 2 2 cos2 cos sin 2cos 1 1 2sin    = - = - = - 2 1 cos2 sin 2   - Þ =   2 1 cos2 cos 2   + = 3 sin3 3sin 4sin  = -  3 cos3 4cos 3cos  = -  2.'()**9.*:. 2.'()*04;<4'<.'(=('>*( ( ) sin sin .cos cos .sin     ± = ± ( ) cos cos .cos sin .sin     ± = m ( ) tan tan tan 1 tan .tan       + + = - ( ) tan tan tan 1 tan .tan       - - = + cos cos 2cos .cos 2 2       + - + = cos cos 2sin .sin 2 2       + - - = - sin sin 2sin .cos 2 2       + - + = sin sin 2cos .sin 2 2       + - - = 2.'()*04;<4'<.'(=('>*( 2.'()*'>( sin ,cos  '(?@ tan 2   =   !"#$%&'((()$%( *+,-., ( ) ( ) 1 cos .cos cos cos 2 ộ ự = - + + ờ ỳ ở ỷ ( ) ( ) 1 sin .cos sin sin 2 ộ ự = - + + ờ ỳ ở ỷ ( ) ( ) 1 sin .sin cos cos 2 ộ ự = - - + ờ ỳ ở ỷ tan 2 = 2 2 2 2 2 sin 1 1 cos 1 2 tan 1 ỡ ù ù = ù + ù ù ù ù - ù ị = ớ ù + ù ù ù ù = ù ù - ù ợ !9'AB*2.'()*C(D* !9'AB*2.'()*C(D* 4 4 2 1 cos4 cos sin 1 sin 2 1 42 3 + + = - = 6 6 2 3 cos4 cos sin 1 sin 2 3 84 5 + + = - = 2 tan cot sin2 + = cot tan 2cot2 - = sin cos 2sin 2cos 4 4 ổ ử ổ ử ữ ữ ỗ ỗ ữ ữ + = + = - ỗ ỗ ữ ữ ỗ ỗ ữ ữ ỗ ỗ ố ứ ố ứ sin cos 2sin 2cos 4 4 ổ ử ổ ử ữ ữ ỗ ỗ ữ ữ - = - = + ỗ ỗ ữ ữ ỗ ỗ ữ ữ ỗ ỗ ố ứ ố ứ E $FGH#$%FI J(,/.'KL(+,- 4D**/01M J(,/.'KL(+,- 4D**/01M 2 sin sin 2 ộ = + ờ = ờ = - + ờ ở sin 0 sin 1 2 2 sin 1 2 2 ỡ ù ù = ị = ù ù ù ù ù = ị = + ớ ù ù ù ù ù = - ị = - + ù ù ợ 2 cos cos 2 ộ = + ờ = ờ = - + ờ ở cos 0 2 cos 1 2 cos 1 2 ỡ ù ù = ị = + ù ù ù ù = ị = ớ ù ù = - ị = + ù ù ù ù ợ tan tan : , 2 = = + ạ + tan 0 tan 1 4 ỡ ù = = ù ù ù ớ ù = = + ù ù ù ợ cot cot : , = = + ạ cot 0 2 cot 1 4 ỡ ù ù = = + ù ù ù ớ ù ù = = + ù ù ù ợ !"#$% !"#$% ( ) sin cos 1 + = &'()* 2 2 2 + +,, 2 2 + /," ( ) 2 2 2 2 2 2 1 sin cos + = + + + ( ) 2 2 2 2 sin , cos 0, 2 ộ ự = = ẻ ờ ỳ ở ỷ + + 01 2 2 2 2 sin .sin cos .cos cos( ) cos + = - = = + + 2 ( ) = + ẻ Â   !"#$%&'((()$%( *+,-.,      !"2345,$%  !"2345,$% ( )  2 2 sin sin cos cos 2       + + =  6#*,78* cos 0 = )491*,:(;<.')5*1:  6 cos 0 ¹ /,, 4 ( ) 2  2 cos  /,"  2 2 .tan .tan (1 tan )      + + = +   tan = /",-&45,8   2 ( ) . 0       - + + - = ® ®   "=7>$% "=7>$% ( ) ( ) sin cos sin cos 0 3      ± + + =   ( ) cos sin 2.cos ; 2 4       = ± = £m  2 2 1 1 2sin .cos sin .cos ( 1) 2      Þ = ± Þ = ± -  ?,:-14 ( ) 3 /," 45,8   ® ®     "=7>$% "=7>$% ( ) sin cos sin cos 0 4      ± + + =   ( ) 2 1 cos sin 2. cos ; : 0 2 sin .cos ( 1) 4 2           = ± = £ £ Þ = ± -m  @9A$%B6*  C'D4>,$3'E':"= N $FGHOP J J (,/.'KL(08*(64 (,/.'KL(08*(64M ( )  2 0 1  + + =     ;:  +=AB+Q ;:  +=AB*(R ?F 2 4 D = -  <.' 0D < Þ -*  <.' 0D = Þ )* (G4 2    = -   <.' 0D > Þ ), *4H 1 2 2 2       é - - D ê = ê ê ê - + D ê = ê ë ?F 2 ' ' D = - -I ' 2   =  <.' ' 0D < Þ -*  <.' ' 0D = Þ )* (G4 '   = -   <.' ' 0D > Þ ),* 4H 1 2 ' ' ' '       é - - D ê = ê ê ê - + D ê = ê ë     <.'4 ( ) 1 ),*4H 1 2 ,    ?,* 1 2      = + = -  ?F,* 1 2 .      = =    !"#  !"#  ( 1 2 2 '     D D Þ - = =   !"#$%&'((()$%( *+,-.,   ),*4H 0 0  ¹ ì ï ï Û í ï D > ï î ),*!$3' . 0Û < ),*4HJ$3' 0 0 ì D > ï ï Û í ï > ï î ),*H*4H 0 0 0   ì ï D > ï ï ï ï Û > í ï ï ï < ï ï î ),*$4H 0 0 0   ì ï D > ï ï ï ï Û > í ï ï ï > ï ï î   $%& !"# $%& !"#       2 ( ) 0    = + + =   -IK= -IK=     β β 3( 3(  ( ) 2 1 0 . 0 2        ì ï ï ï D > ï ï ï > > Û > í ï ï ï ï > ï ï î  ( )   1 2 0 . 0 2        ì ï ï ï D > ï ï ï < < Û > í ï ï ï ï < ï ï î  ( ) 1 2 . 0   < < Û < "J "J (,/.'KL(08*EM (,/.'KL(08*EM   ( )  3 2 ' ' ' 0 2     + + + =  ( ) ( )  2 2 ( ) 0 0 3           = é ê Û - + + = Û ê + + = ê ë     2 2 ( ) , 4      = + + D = -   ( ) 2 )*4H ( ) 3Û )*4H 0 ( ) 0     ì D > ï ï ï ¹ Û í ï ¹ ï ï î  ( ) 2 )*4H ( ) 3Û )*(G4  ¹  ( ) 3 ),* 4H"))K*  = 0 ( ) 0 0 ( ) 0     é ì D = ï ï ê ï í ê ï ¹ ê ï ï î ê Û ê ì D > ï ê ï ï í ê ï = ê ï ï î ë  ( ) 2 )K* ( ) 3Û -* ( ) 3 )*(G4  = 0 ( ) 0 0   é ì D = ï ï ê ï í ê ï = Û ê ï ï î ê ê D < ê ë EJ EJ (,/.'KL(08*0B'KS.T(,/. (,/.'KL(08*0B'KS.T(,/. ( )  4 2 0 4  + + =   2 . : 0   = ³  ( ) ( )  2 4 0 5  Û + + =  /   !"#$%&'((()$%( *+,-.,    ( ) 4 )*4H ( ) 5Û )*$4H 0 0 0   ì ï D > ï ï ï ï Û > í ï ï ï > ï ï î  ( ) 4 )*4H ( ) 5Û )K* 0 = -1K* 0 0 0     ì ï = ï ï ï > Û í ï - > ï ï ï î  ( ) 4 )*4H ( ) 5Û )*!$3' ( ) 5 )*(G4 $ 0 0 0   < é ê ê ì D = ï Û ê ï ê í ï > ê ï î ë NJ NJ (,/.'KL(*()6*U'()* (,/.'KL(*()6*U'()*MV 2 0     ì ³ ï ï ï = Û í ï = ï ï î V ( )  0 0       ì ³ ³ ï ï ï = Û í ï = ï ï î WJ WJ (,/.'KL(*()6X:.4D'KY':Z&'B4M (,/.'KL(*()6X:.4D'KY':Z&'B4M   V V 0     ì ³ ï ï = Û í ï = ± ï î  V V      = Û = ± [J [J I'T(,/.'KL(*()6*U'()* I'T(,/.'KL(*()6*U'()* M M V V 2 0 0 0        é ì < ï ï ê í ê ï ³ ê ï î ê ³ Û ê ì ³ ï ê ï ï í ê ï ³ ê ï ï î ë  V V   2 0 0       ì ï ³ ï ï ï ï £ Û ³ í ï ï ï £ ï ï î \J \J I'T(,/.'KL(*()6X:.4D'KY':Z&'B4 I'T(,/.'KL(*()6X:.4D'KY':Z&'B4 M M   V V     £ Û - £ £  V V       é ³ ê ³ Û ê £ - ê ë W H]^ ?*42L8,   o M="#* ( ) ,      / ( ) ,      / ( ) ,      -1 ( ) ,      o N2 : 0  D + + =  o NO ( ) ( ) ( )   2 2 2 2 :( ) : 2 2 0               - + - = + - - + = )H*1 ( ) ,   -1!(F1 2 2    = + -   PG ( ) ;         = - - Þ uuur Q$1"%2 ( ) ( ) 2 2         = - + -  '(% )*+"R,M-  #,"#* ( ) ,       ( ) ,      -1 ( ) ,      21                 - - Û = - -   69!S"#* ( ) ,      "."N2 : 0  D + + = 1 ( ) 2 2 ,          + + D = +  #R-1M"=7>,'T',"N2 D Û D 1"N2'AU,"%2RM  LFVRM+ ( ) 2 2 2 1 1 . .sin . . 2 2          D = = - uuur uuur  0   !"#$%&'((()$%( *+,-.,    ( ) ( ) ( ) 1 1 1 . . . 2 2 2 4                 = - - - = = = = = ?") , ,   C 1!(F"NO%.4/!(F"NOQ.4-1W,'-  #R-1MX*-&4F,(!4F,-I"N2 ( ) ( ) . 0          D Û + + + + <   #R-1MX*-&J4F,-I"N2 ( ) ( ) . 0          D Û + + + + >   #R-1MJX*"NO,:JX*1"NO ( ) ( ) 2 2 2 2 / ( ) / ( ) . 0 2 2 2 2 0                        Û > Û + - - + + - - + >   #R-1MX*-&,4F,(!,'"=-I"NOK"#*4F,/*Q"#*4F,1 ( ) ( ) 2 2 2 2 / ( ) /( ) . 0 2 2 2 2 0                        Û < Û + - - + + - - + < $F  !O _`abc !OP  I  Fdebc !OP /Af+g'(:Z;' JY(.(h6M YZ1*= ( )  = "[.B 1 2 ,   Û " Î -1 1 2 1 2 ( ) ( )     < Þ <  YZ1*= ( )  = E.B 1 2 ,   Û " Î -1 1 2 1 2 ( ) ( )     < Þ >  "J4:C4&*iM@9W ( )  = )"%1*B(9\ Y<.' ( )  = "[.B(9\ '( ) 0,   ³ " Î  Y<.' ( )  = E.B(9\ '( ) 0,   £ " Î  EJ4:C4&jM@9W ( )  = )"%1*B(9\ Y<.' ' '( ) 0  = ³ /  " Î ] '( ) 0  = %K=^'%"#*_ ( )  = "[.B\ Y<.' ' '( ) 0  = £ /  " Î ] '( ) 0  = %K=^'%"#*_ ( )  = E.B\ Y<.' ' '( ) 0  = = / ( )  = ("B\ 12#<.'(9\" ,:0@7k6C(@1. ( )  = T(14+4l'm*B")  noFdep'LqC(@1.'U.r.41qsbc !OP ( ) . / 0=  J(,/.T(DT.414 345#?*547!"EU,1*=?N4!N 4,'  6   !"#$%&'((()$%( *+,-.,   ` ( ) : ( ) 0 ( )      !  !  = Þ ¹ ` ( ) : ( ) 0 !    ! = Þ ³ ` ( ) : ( ) 0 ( )      !  !  = Þ > 345#?*!"#*%") ' '( ) 0  = =  ' '( )  = (7!"E/a,1*"%1* ' '( )  = + ' '( ) 0  = =  ** "  -I ( )  1; 2; 3 " #=  345(#bc47.4!"#*")8>Ad$C-1549.B"#7G$3' ' '( )  =  345/#LA,-19.B/(.'5!(9"[.-1E.U,1*= ` '( ) ' 0  = ³ Þ Z1*="[.dB(9ee-1ee ` '( ) ' 0  = < Þ Z1*=E.9*B(9e-1ee "J!9'AB+,:gC(4.414'@D V#,:g=-I1*4H>^'f$3'ghi(79:, V#,:g" •=-I1*$%      + = + 1*='"[.E.B?j/a,1' *"  ' 0 >  ' 0 < B?j •=-I1*$% 2 ' '        + + = + ')F3,(9""' • =-I1*$%  4 3 2      = + + + +  ')F3*Q(9"[.-1*Q (9E. •+9,1*=BC(2.'(t'/4&:'Kl ¡  V#,:gEM97G$3'*Q=1*N4 6s(Y'()*08*('M ( ) /( ) 0     = = + ¹    −∞    - 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= Þ = = + + + +!I?F"NGFSF"NG4n ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 ' ' ' ' ' ' ' ' 2 ' ' ' ' ' ' ' ' ' ' ' ' ' '                                                 + + - + - + - + + = Þ = = + + + + + + Β◊ι 1. ?*!(9""'U,!1*= ,o 4 2 4 3  = - + -  o 4 2 6 8 1   = - + +  o 4 4 6  = + +  $o 3 2 6 9 4   = - + - +  8o 3 2 3 3 2   = + + +  po 2 2  = -  o 2 1 1    - = -  o 3 1 1    + = -  o 3 2 7    - = +  Β◊ι 2. ?*!(9""'U,!1*= ,o 2 2 1 2     - + - = +  o 2 8 9 5     - + = -  o 2 2 3     + = - +  $o ( ) 2 4 3 6 1  = - +  8o 2 1 2 3 3   = + - + +  po 3 2 2  = -  Β◊ι 3. ?*!(9""'U,!1*= ,o 2 5 6  = + +  o 2 1 2 5 7   = - + - + -  o 2 4  = -  $o 2 2 3  = + +  8o 3 2 7 7 15   = - - +  po 2 2 3 3 2     - + = +  Β◊ι 4. ?*!(9""'U,!1*=,' ,o  sin , 0;     é ù = - Î ê ú ë û  o  2sin cos2 , 0;     é ù = + Î ê ú ë û  o   2 sin cos , 0;    é ù = + ê ú ë û  $o 3 sin cos2 sin 2   = - + +  8o   2 sin cos 1, 0; 2      é ù = + + Î ê ú ê ú ë û  po [ ]  3 4 2sin sin , 0; 3     = - Î Β◊ι 5. +>*X ,oZ1*= 3 cos 4   = + - - "[.B ¡  oZ1*= 2sin tan 3   = + -  "[.BW,(9 ) 0; 2  é ê ë  " Lq4:C4&*j6'(6qABt(=qAB ( ) . / 0= w.04;(@x*.(Y*(04; J/Af+g'(:Z;' +1*= ( ) ,   = -I  1,*=/)547!"EL •Z1*= ( ) ,   = "[.BL Û  ' 0 ³  " Î L •Z1*= ( ) ,   = E.BL Û  ' 0 £ /  " Î L •Z1*= ( ) ,   = "[.B ¡  ' '( , ) 0, min ' 0        Î Û = ³ " Î Û ³ ¡ ¡  ' +!Ic0%U*!(64C0q*%: ?,*=   !"#$%&'((()$%( *+,-.,   •Z1*= ( ) ,   = E.B ¡  ' '( , ) 0, max ' 0        Î Û = £ " Î Û £ ¡ ¡ •Z1*="[.B ¡ )497!"EB ¡  J(,/.T(DT.414 7.<.' 2 ' '( , )      = = + +  •#1*= ( ) ,   = "[.dB  0 ' '( , ) 0; 0       ì ï > ï Û = ³ " Î Û í ï D £ ï î ¡ ¡ •#1*= ( ) ,   = E.9*B  0 ' '( , ) 0; 0       ì ï < ï Û = £ " Î Û í ï D £ ï î ¡ ¡ 12#1234"5&1)6789(:0. 7."<.' [ ]  ' ; ;     = + " Î  •#1*= ( ) ,   = "[.B [ ] ;  [ ]   '( ) 0 ' 0; ; '( ) 0         ì ³ ï ï ï Û ³ " Î Û í ï ³ ï ï î •#1*= ( ) ,   = E.B [ ] ;  [ ]   '( ) 0 ' 0; ; '( ) 0         ì £ ï ï ï Û £ " Î Û í ï £ ï ï î 7.E<.' 2 ' '( )     = = + +  ' '( )  = 1*Q1*3(r1(!/*1,C ' '( ) 0  = ³ ,: ' '( ) 0  = £ B(9 ( ) ,  "% [ ] ,  BW,"%,:W,(9 1")?,1*8!I,' •I,y*?**&7!"EU, ' '( )  =  •I,y*"Q54!  ,:#'>>,  ,(q.  -1':#  -&*Q  O% 1 ( )  s'D(':# 14H>49"#D"&'(7!"EU,#'>"#(7G$3' '( )   ,",-197G$3' '( )    •I,y*E?F '( )  + '( ) 0  = -1**  •I,y*Ns549.BU, '( )    •I,y*W6.'5z#y(/AB+y5Iv(/AB0v{<a,1 Y(," ( )   ³ $A,-19.B,t3:!E  ³ AB+y('9.B Y(," ( )   £ $A,-19.B,t3:!E  £ AB(|('9.B 7.N?*  "#1*&1 3 2     = + + + )"Q$1(9"[.E. =  ?,9,'  •I,y*?F ' '( )  =   •I,y*"?*"&'("#1*=)(9"[.-1E. ( )  0 1 0  ¹ ì ï ï í ï D > ï î   •I,y*EM." 1 2   - = 1 ( ) ( )  2 2 1 2 1 2 4 . 2    - - =  •I,y*NbW$n"EDPG",148   •I,y*W@94/-I"&'(K"#l* J!9'AB+,:gC(4.414'@D •#,:g+CW$n1%"EFPG-1!*U,45,-I=β  %   !"#$%&'((()$%( *+,-.,   •#,:g"?,)#$J$%!%"#91!*,*=  U,*Q34* "&'("#4)*/-*K//e*/e I=4J ?*,*=  "#1*= ,o 3 2 3 3( 2) 3 1     = - + + + - "[.B ¡  o ( ) ( ) 3 2 2 1 2 2     = - - + - + "[.B ¡  o ( ) 3 2 3 2 2    = + - + + "[.B547!"EU,) $o ( ) 3 2 2 2 3 3 1 3 1     = - + + - - - '9* 8o ( ) ( ) ( ) 3 2 1 3 3 2 3 3       = - - + + + - 'dB ¡  po ( ) ( ) 2 3 2 1 1 1 3 5 3      = - + + + + '"[.B ¡  DTABM,o 1 ³ - o 5 1 4 - £ £ o 6 3 3;6 3 3 é ù Î - + ê ú ë û $o 0 = 8o 3 1 2 - £ £ - po ( ) ) ; 1 2; é Î - ¥ - È +¥ ê ë I=4"J ?*,*=  "#1*= ,o 3 2     + - = + 'E.B*u547!"EU,) o 2 1     - = - + "[.BS(97!"EU,) o 2 1    + = + E.BS(97!"EU,) $o ( ) 2 2 2 3 1 1       - + + - + = - E.BS(97!"EU,) DTABM,o 3 1- < < o 1 2- < < o 1 1 2 2 - < < $o 1 2  £ I=4EJ ?*,*=  "#1*= ,o ( ) 3 2 2 1 1    = - - + + "[.B"% 0;2 é ù ê ú ë û  o ( ) 3 2 3 1 4     = + + + + E.B(9 ( ) 1;1-  o 3 2 3 4   = + - - "[.B(9 ( ) 0;+¥  $o ( ) 3 2 1 2 1 2 3      = - + - - + E.B(9 ( ) 2;0-  8o 4    + = + E.B(9 ( ) ;1- ¥  po 2 6 2 2     + - = + E.BW,(9 ) 1; é +¥ ê ë  o cos   = + "[.B ¡  DTABM,o 1 £ - o 10 £ - o 0 £ $o 1 2  ³ 8o 3 2 2 - £ £ po 2 1- < <- o 14 5  £ - o 1 1- £ £ I=4NJ ?*,*=  "#1*= ,o ( ) ( ) 3 2 2 2 1 2 3 2 2        = - + - - + + - "[.BW,(9 ) 2; é +¥ ê ë  o  K   "0""0"0. −+++++= "[.BW,(9 ) 1; é +¥ ê ë   $ [...]... m - 1) x Tim m ờ ham sụ co 2 cc tri thoa: 3 2 2 x1 = x2 + 3 Trang 22 Chuyờn kho sỏt hm s 12 Trung tõm luyn thi Trớ Tu Nha Trang b/ Cho ham sụ y = Trng Ngc V -Nha trang T:0978333.093 1 3 m mx - mx2 + ( m2 - 1) x Tim m ờ ham sụ co 2 cc tri thoa: 3 3 2 x1 = x1.( x2 - 5) + 12 c/ Cho ham sụ y = 2x3 + 9mx2 + 12 2x + 1 Tim m ờ ham sụ co 2 cc tri, ng thi 2 hoanh ụ cc tri m 2 thoa: xCé = xCT 15 Tim tham... - 4x + 5 x2 - 4x + m co nghiờm thc trong oan ờ ỳ ở ỷ ap sụ: a/ m 3 2 1 b/ - 2 < m < 2 6 2 Tim tham sụ thc m ờ phng trinh: a/ x 2 + mx + 2 = 2 x + 1 co hai nghiờm phõn biờt Trang 12 c/ m Ê - 1 Chuyờn kho sỏt hm s 12 Trung tõm luyn thi Trớ Tu Nha Trang b/ Trng Ngc V -Nha trang T:0978333.093 x + 9 x = x 2 + 9 x + m co nghiờm c/ 3 x 1 + m x + 1 = 2 4 x 2 1 co nghiờm d/ 6 x + x + 3 = mx co nghiờm... 21 Chuyờn kho sỏt hm s 12 Trung tõm luyn thi Trớ Tu Nha Trang Trng Ngc V -Nha trang T:0978333.093 3 2 7 Tim m ờ thi ham sụ y = x - 3x + 2 (C ) co iờm cc ai va iờm cc tiờu cua thi ( C ) nm vờ hai phia khac nhau cua mụt ng tron (phia trong ng tron va phia ngoai ng tron): (C ) : x 2 m + y2 - 2mx - 4my + 5m2 - 1 = 0 3 1x 6x2 1 x2 1 f 1 + x < 1 + x < 1 + x, " x > 0 2 8 2 4x ổ pử 2 h 28/ sin x < 2 ( p - x) , " x ẻ ỗ0 ữ ỗ ; 2ữ ố ứ p b sin x < x - DNG 4 ng dng tinh n iờu giai phng trinh bt phng trinh cú cha tham sụ m ( ) Bai toan 1 Tim m ờ phng trinh f x;m = 0 co nghiờm trờn D ? Trang 11 Chuyờn kho sỏt hm s 12 Trung tõm luyn thi Trớ Tu Nha Trang... khụng xet dõu c nh bõc 1, bõc 2 thi chon iờm ờ xet dõu Bai 1 Tim cc tri cua cac ham sụ sau: a/ y = x3 + 3x2 + 3x + 5 b/ y = x3 + 3x2 - 9x + 4 Trang 14 c/ y = - 2 3 5 2 x + x - 2x 3 2 Chuyờn kho sỏt hm s 12 Trung tõm luyn thi Trớ Tu Nha Trang d/ y = Trng Ngc V -Nha trang T:0978333.093 4 3 x - 6x2 + 9x - 1 3 e/ y = - x4 + 6x2 - 8x + 1 ( ) ( ) () b/ yCé = y - 3 = 31; yCT = y 1 = - 1 ap sụ:a/ Ham sụ khụng... Bai 2 Tim cc tri cua cac ham sụ sau: a/ y = 3 - 2x x- 1 b/ y = 3x + 1 1- x c/ y = - x2 + 2x - 1 x +2 d/ y = ap sụ:a/ Ham sụ khụng co cc tri b/ Ham sụ khụng co cc tri c/ yCé = y 1 = 0 ; yCT = y - 5 = 12 x2 - 8x + 9 x- 5 d/ Ham sụ khụng co cc tri () ( ) Bai 3 Tim cc tri cua cac ham sụ: a/ y = - x3 + 3x2 b/ y = x 4 - x2 d/ y = 2x + 1- e/ y = x x + 2 ( 2x2 - 8 c/ y = 2x - ) ( ( ) ( ) ( ) c/ y = 3 - 2cosx... k = b/ yCé = y ỗ + kpữ - 1 yCT = y ỗ + ( 2 + 1) ữ - 5 ỗ ỗ ữ ữ ỗ4 ữ ữ ỗ4 2ứ ố ứ ố ổ 2p ử 9 ữ c/ yCé = y ỗ ữ ỗ 3 + k2pứ= 2 yCT = y ( kp) = 2( 1- coskp) ữ ố 4 1 d/ Ham sụ at cc ai tai x = b ; y ( b) = 12 vi sin b = 3 3 1 ữ = a/ yCé = y ỗ + kpữ ỗ ữ ỗ6 ữ ố ứ 2 DNG 2 TIM THAM Sễ m HM Sễ Cể CC TR TI x0 Bai toan 1: Cho ham sụ y = f (x, m) Tim tham sụ m ờ ham sụ at cc tri tai iờm x = x0 Phng phap giai... ' = f '(x, m) + ờ ham sụ at cc tri tai x = x0 thi: f '(x0, m) = 0 ị m Bai toan 2: Cho ham sụ y = f (x, m) Tim tham sụ m ờ ham sụ at cc ai tai iờm x = x0 Phng phap giai Trang 15 Chuyờn kho sỏt hm s 12 Trung tõm luyn thi Trớ Tu Nha Trang Trng Ngc V -Nha trang T:0978333.093 + Tim tõp xac inh + Tinh y ' = f '(x, m);y '' = f ''(x, m) ( ) ù f ''( x , m) < 0 ù ù ợ ỡ f ' x ,m = 0 ù ù 0 ị m + ờ ham sụ at... sụ ờ ham sụ: 3 mx2 + 3( m2 - 1) x + m at cc ai tai x = 2 a/ y = x - 3 2 m 3 mx2 + 6x - 6 at cc tiờu tai x = 1 b/ y = - ( m + 5 ) x + 6 c/ y = x3 - 2x2 + mx + 1 at cc tiờu tai x = 1 d/ y = mx3 + 3x2 + 12x + 2 at cc ai tai iờm x = 2 x2 + mx + 1 e/ y = at cc ai tai x = 2 x +m ap sụ a/ m = 3 b/ m = - 2 c/ m = 1 d/ m = - 2 e/ m = - 3 Bai 2 Tim tham sụ m ờ ham sụ: a/ y = 1 3 x - mx2 + ( m2 - m + 1) x +... tham sụ a,b ờ ham sụ: x4 + ax2 + b co cc tri tai x = - 1 va gia tri cc tri tng ng cua ham sụ bng - 2 4 5 2 3 5 ax2 - 9x + b co gia tri cc tri la nhng sụ dng va xo = b/ y = a x + 2 la iờm cc ai 3 9 1 9 9 128 9 140 ap sụ:a/ a = - ;b = b/ a = hoc a = ; b ; b 2 4 25 27 5 27 a/ y = Bai 4 Tim gia tri cua tham sụ ờ ham sụ : a/ y = x3 + mx2 + ( m + 1 x - 1 co cc tri tai x = 2 Khi o ham sụ at cc ai hay cc tiờu . ứ I=4"J +>*X , 2 1 sin tan , 0; 3 3 2 ổ ử ữ ỗ + > " ẻ ữ ỗ ữ ố ứ / 3 5 sin 0 6 120 < - + " > ( ) / 2 sin 0; 2 > " ẻ $ ( ) 2 1 1 sin 1 , 0; 6 . 1 1 + = - o 2 2 1 2 - + - = + $o 2 8 9 5 - + = - DTABM,oZ1*=()AE oZ1*=()AE o ( ) 1 0 = = ( ) 5 12 = - = $oZ1*=()AE I=4EJ ?*AEU,!1*= ,o 3 2 3 = - + o 2 4 = - o 2 2 3 = - - $o 2 2 1 2 8 . 2 ổ ử ữ ỗ = + = ữ ỗ ữ ỗ ố ứ ( ) ( ) 2 1 cos = = - $oZ1*="%A"%% = ( ) 4 12 3 = -I 1 sin 3 = " H!c!OP !OP~Ga 0 I=4'@DM+1*= ( , ) = ?*,*= "#1*="%**'KY%"#* 0