函數(shù)零點(diǎn)問(wèn)題

1、1函數(shù)零點(diǎn)問(wèn)題函數(shù)零點(diǎn)問(wèn)題數(shù)學(xué)原理數(shù)學(xué)原理1.區(qū)間根存在原理若函數(shù)在內(nèi)的圖像是一條連續(xù)的曲線，且，則函數(shù)()yfx?()ab()()0fafb??在內(nèi)有零點(diǎn)，即存在，使得.()yfx?()ab()cab?()0fc?2.函數(shù)零點(diǎn)的個(gè)數(shù)問(wèn)題可以轉(zhuǎn)化為函數(shù)圖象的交點(diǎn)個(gè)數(shù)問(wèn)題（數(shù)形結(jié)合思想）；函數(shù)零點(diǎn)所屬區(qū)間可通過(guò)區(qū)間根存在原理進(jìn)行判定.數(shù)學(xué)應(yīng)用數(shù)學(xué)應(yīng)用1.一元二次函數(shù)的零點(diǎn)問(wèn)題一元二次函數(shù)的零點(diǎn)問(wèn)題1.1如果函數(shù)至多有一個(gè)零點(diǎn)，則的取值范圍

2、是________.2(3)yxmxm????m1.2無(wú)論取何值時(shí)，方程總有2個(gè)相異實(shí)根，則的取值范圍是k254()xxkxa????a________________.1.3已知是方程的兩個(gè)根，且，則的取值范??2(21)420xmxm?????2????m圍是____________.1.4已知的方程的一根分步在區(qū)間內(nèi)，另一根分步在區(qū)間x2350xxa???(20)?內(nèi)，則實(shí)數(shù)的取值范圍是____________.(13)a2.零點(diǎn)

3、個(gè)數(shù)問(wèn)題零點(diǎn)個(gè)數(shù)問(wèn)題2.1函數(shù)的零點(diǎn)個(gè)數(shù)是___________.3()231fxxx???2.2函數(shù)的零點(diǎn)個(gè)數(shù)是___________.()lgsinfxxx??2.3已知定義在R上的奇函數(shù)滿足，且在區(qū)間上是增函數(shù).若()fx(4)()fxfx???[02]33.函數(shù)零點(diǎn)所屬區(qū)間問(wèn)題函數(shù)零點(diǎn)所屬區(qū)間問(wèn)題3.1若方程在區(qū)間上有一根，則310xx???()(1)ababZba???且_______.ab??3.2設(shè)下列結(jié)論中正確的是___

4、_____(填序號(hào)).)2(1)(?????nNnxxxfnn①在內(nèi)不存在零點(diǎn)；②在內(nèi)存在唯一零點(diǎn)；3()fx??????1214()fx??????121③設(shè)為函數(shù)在內(nèi)的零點(diǎn)，則)4(?nxn()nfx??????121.1??nnxx3.3設(shè)20134321)(20134321)(20134322013432xxxxxxgxxxxxxf????????????????????令若的零點(diǎn)均在區(qū)間內(nèi)，則)4()3()(???xgxfxF