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hamhuuti - Bai 2 ON TAP VE HAM HU TY(Noi dung on tap do...

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Baøi 2: OÂN TAÄP VEÀ HAØM HÖÕU TYÛ (Noäi dung oân taäp do trung taâm luyeän thi chaát löôïng cao Vónh Vieãn cung caáp) 1) Phöông trình toång quaùt : f(x) = p mx c bx ax 2 + + + vôùi a.m 0. Thöïc hieän pheùp chia ña thöùc ta coù : f(x) = p mx D m ap bm x m a 2 + + + ( 1 ) Vôùi D = c – p 2 bm ap m 2) Ñöôøng tieäm caän : * Neáu D 0 ñoà thò haøm soá coù ñöôøng tieäm caän ñöùng x = m p vaø tieäm caän xieân y = 2 m ap bm x m a + . Giao ñieåm I cuûa hai tieäm caän laø taâm ñoái xöùng cuûa ñoà thò haøm soá. * Neáu D = 0, ñoà thò suy bieán thaønh ñöôøng thaúng y = 2 m ap bm x m a + tröø moät ñieåm coù hoaønh ñoä x = m p . 3) Ñaïo haøm caáp 1, 2 : Khi gaëp haøm höõu tæ neân duøng coâng thöùc (1), ta coù : f’(x) = 2 2 2 ) p mx ( Dm ) p mx ( m a ) p mx ( Dm m a + + = + / / 3 .2 ( ) ( ) Dm m f x mx p = + 4) Cöïc trò haøm soá : Neáu tam thöùc g(x) = Dm ) p mx ( m a 2 + coù hai nghieäm phaân bieät x 1 , x 2 thì haøm soá ñaït cöïc trò taïi x 1 , x 2 vaø ñoà thò haøm soá coù hai ñieåm cöïc trò laø : M + m b x m a 2 , x 1 1 N + m b x m a 2 , x 2 2 i) Neáu a.m > 0 vaø y / = 0 voâ nghieäm thì haøm taêng ( ñoàng bieán) treân töøng khoûang xaùc ñònh. ii) Neáu a.m < 0 vaø y / = 0 voâ nghieäm thì haøm giaûm ( nghòch bieán) treân töøng khoûang xaùc ñònh. iii) Neáu a.m > 0 vaø y / = 0 coù 2 nghieäm phaân bieät x 1 , x 2 thì haøm ñaït cöïc ñaïi taïi x 1 vaø ñaït cöïc tieåu taïi x 2 thoûa x 1 < x 2 vaø 1 2 x x p 2 m + =− . iv) Neáu a.m < 0 vaø y / = 0 coù 2 nghieäm phaân bieät x 1 , x 2 thì haøm ñaït cöïc tieåu taïi x 1 vaø ñaït cöïc ñaïi taïi x 2 thoûa x 1 < x 2 vaø 1 2 x x p 2 m + =− . 5) Phöông trình ñöôøng thaúng qua hai ñieåm cöïc trò : Giaû söû haøm coù cöïc trò. Toïa ñoä hai ñieåm cöïc trò thoûa phöông trình ñöôøng thaúng : y = m b x m a 2 + ñoù laø phöông trình ñöôøng thaúng ñi qua 2 ñieåm cöïc trò. 6) Tính chaát cuûa tieáp tuyeán :
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Moïi tieáp tuyeán vôùi (C) taïi M thuoäc ( C ) caét hai ñöôøng tieäm caän taïi A vaø B thì : * M laø trung ñieåm AB. * Tam giaùc IAB coù dieän tích khoâng ñoåi. 7) Tính chaát cuûa ñöôøng tieäm caän : * Moïi ñieåm M thuoäc (C) coù tích hai khoaûng caùch töø M ñeán hai ñöôøng tieäm caän laø moät haèng soá. * Neáu töø moät ñieåm E naèm treân moät ñöôøng tieäm caän cuûa (C) thì qua E chæ coù moät tieáp tuyeán duy nhaát vôùi (C). 8) Khi a = 0 vaø m 0 ta coù haøm nhaát bieán f(x) = bx c mx p + + * Khi m 0 vaø bp – cm 0 thì ñoà thò haøm soá coù ñöôøng tieäm caän ñöùng x = m p vaø tieäm caän ngang laø y = b m .
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