Ontaphamsobac3(2)

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Unformatted text preview: ON TAP VE HAM SO BAC 3 (Trung tam Luyen thi ai hoc Vnh Vien) Gia s : y = ax 3 + bx 2 + cx + d vi a 0 co o th la (C). y = 3ax 2 + 2bx + c, y = 6ax + 2b 1) y = 0 x = a 3 b- (a 0 ) x = a 3 b- la hoanh o iem uon. o th ham bac 3 nhan iem uon lam tam oi xng. 2) e ve o th 1 ham so bac 3, ta ca n biet cac trng hp sau : i) a > 0 va y = 0 vo nghiem ham so tang tren R (luon luon tang) ii) a < 0 va y = 0 vo nghiem ham so giam (nghch bien) tren R (luon luon giam) iii) a > 0 va y = 0 co 2 nghiem phan biet x 1 , x 2 vi x 1 < x 2 ham so at cc ai tai x 1 va at cc tieu tai x 2 . Ngoai ra ta con co : + x 1 + x 2 = 2x vi x la hoanh o iem uon. + ham so tang tren (- , x 1 ) + ham so tang tren (x 2 , + ) + ham so giam tren (x 1 , x 2 ) iv) a < 0 va y = 0 co 2 nghiem phan biet x 1 , x 2 vi x 1 < x 2 ham at cc tieu tai x 1 va at cc ai tai x 2 thoa ie u kien x 1 + x 2 = 2x (x la hoanh o iem uon). Ta cung co : + ham so giam tren (- , x 1 ) + ham so giam tren (x 2 , + ) + ham so tang tren (x 1 , x 2 ) 3) Gia s y = 0 co 2 nghiem phan biet va y = k(Ax + B)y + r x + q vi k la hang so khac 0; th phng trnh ng thang qua 2 iem cc tr la y = r x + q 4) (C) cat Ox tai 3 iem phan biet < = ) 2 x ( y ). 1 x ( y 2 x , 1 x biet an nghiem ph 2 co ' y 5) Gia s a > 0 ta co : i) (C) cat Ox tai 3 iem phan biet > < < < < = ) 2 x ( y ). 1 x ( y ) ( y 2 x 1 x thoa biet an nghiem ph 2 co ' y ii) (C) cat Ox tai 3 iem phan biet < < < < = ) 2 x ( y ). 1 x ( y ) ( y 2 x 1 x thoa biet an nghiem ph 2 co ' y Tng t khi a < 0 . 6) Tiep tuyen : Goi I la iem uon. Cho M (C). Neu M I th ta co ung 1 tiep tuyen qua M. Neu M khac I th ta co ung 2 tiep tuyen qua M. Bien luan so tiep tuyen qua 1 iem N khong nam tren (C) ta co nhie u trng hp hn. 7) (C) cat Ox tai 3 iem phan biet cach e u nhau y = 0 co 2 nghiem phan biet va y(x ) = 0 (x la hoanh o iem uon) 8) Bien luan so nghiem cua phng trnh : ax 3 + bx 2 + cx + d = 0 (1) (a 0) khi x = la 1 nghiem cua (1)....
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