Generated by Foxit PDF Creator â Foxit Software http://www.foxitsoftware.com For evaluation only Lờ Quang Dng THPT s Phự Cỏt , Bỡnh nh LUYN THI I HC 2011- CHIU BIN THIấN C C TR Hm s f(x) ng bin trờn (a,b) f(x) , x thuc (a,b) Hm s f(x) nghch bin trờn (a,b) f(x) , x thuc (a,b) Bi : Cho hm s y x 3x mx , m l tham s ,Tỡm m : a)Hm s ng bin trờn R b) Hm s ng bin trờn (3,+oo) c) Hm s nghch bin trờn (1,3) HD : 2 D=R , y ' 3x 6x m 2 a) Hm s ng bin trờn R y x 0, x R 3x 6x m 0, x R 3m m 2 b) Hm s ng bin trờn (3,+oo) y x 0, x 3, 3x 6x m 0, x 3, m 3x 6x, x 3, Ta cú g(x)= 3x 6x , g(x)=-6x+6 , g(x)=0 x=1=> m g(3) g(x), x 3, Giỏ tr cn tỡm l m 2 c) Hm s nghch bin trờn (1,3) y x 0, x 1, 3x 6x m 0, x 1,3 m 3x 6x, x 1,3 Ta cú g(x)= 3x 6x , g(x)=-6x+6 , g(x)=0 x=1=> m g(3) g(x), x 1, Giỏ tr cn tỡm l m Bi : mx 2mx 14x ,nghch bin trờn (1,+oo) x b) nh m hm s y ng bin trờn(1,+oo) 2x m a)nh m hm s y HD: D=R, y ' mx 4mx 14 Hm s nghch bin trờn (1,+oo) y x 0, x 1, mx 4mx 14 0, x 1, 14 g(x), x 1, x 4x 14(2x 4) 14 0, x 1, => g(x) g(1) , x 1, Ta cú g '(x) 2 (x 4x) 14 Giỏ tr m cn tỡm l : m m m2 b) D R \ ,y x 2x m Hm s ng bin trờn (1,+oo) y(x) , x thuc (1,+oo) m+2>0 , -m/2 -2 2 Bi : a) Tỡm m hm s y x 3x 3( m 1) x 3m cú cc i v cc tiu , v cỏc im cc tr cỏch u gc m ta b) Tỡm m hm s y x 3x mx cú cc i v cc tiu , v cỏc im cc tr cỏch u ng thng y= x+2 c) Xỏc nh m hm s y x 3( m 1) x x m ó cho t cc tr ti x1 , x cho y CT x CD HD: 2 a) D=R , y ' x x 3( m 1) Hm s cú cc i , cc tiu y(x)=0 cú hai nghim phõn bit m khỏc Khi ú y(x)=0 x=1-m,x=1+m Cỏc im cc tr ca th hm s : A(1-m, -2-2m2),B(1+m,-2+2m2) Cỏc im C, CT cỏch u gc ta OA=OB m b) D=R , y ' x x m Generated by Foxit PDF Creator â Foxit Software http://www.foxitsoftware.com For evaluation only Lờ Quang Dng THPT s Phự Cỏt , Bỡnh nh Hm s cú cc i , cc tiu y(x)=0 cú hai nghim phõn bit m 0 y(3)=0 m=1,m=-1 y(3)= 125 m 26 m 18 m=1 , m=9/4 81 (12 10).9 12 26 2 Khi ú m=1 , y(3)=54-18>0 thừa Vy giỏ tr m cn tỡm l : m=1 2 b) D=R , y ' x 4mx x ( x m) Hm s cú C,CT y(x)=0 cú nghim phõn bit x2=m cú nghim phõn bit m>0 Khi ú y(x)=0 x=0, x m Cỏc im cc tr A(0, m4-m2+1) , B1,2 ( m , m 2m ) A,B,C lp thnh mt tam giỏc du AB=AC=BC m+m4 =4m m= 3 c) D=R , y ' x 8mx x( x 4m) Hm s cú C,CT y(x)=0 cú nghim phõn bit x2=-4 m cú nghim phõn bit m .. . r(x) Kt hp iu kin , ta cú giỏ tr m cn tỡm l : m=2 c) Ta có y ' 3x 6( m 1) x +) Hàm số đạt cực đại, cực tiểu x1 , x phương trình y ' có hai nghiệm pb x1 , x Pt x 2(m 1) x có hai nghiệm .. . Generated by Foxit PDF Creator â Foxit Software http://www.foxitsoftware.com For evaluation only Lờ Quang Dng THPT s Phự Cỏt , Bỡnh nh Hm s cú cc i , cc tiu y(x)= 0.. . cho y ta c y(x)=y(x).g(x)+r(x) r x 2(3 (m 1) )x 2m y CT x CD (3 (m 1)2 )(x1 x ) (m 1) ( x x 4x1x )) (m 1)2 (m 1) m (2) Từ (1) (2) suy giá trị m m m x4