函數(shù)應(yīng)用零點(diǎn)二分法知識(shí)點(diǎn)和練習(xí)

(完整word版)(整理)函數(shù)應(yīng)用零點(diǎn)二分法知識(shí)點(diǎn)和練習(xí).(完整word版)(整理)函數(shù)應(yīng)用零點(diǎn)二分法知識(shí)點(diǎn)和練習(xí).精品文檔精品文檔(完整word版)(整理)函數(shù)應(yīng)用零點(diǎn)二分法知識(shí)點(diǎn)和練習(xí).精品文檔一、方程的根與函數(shù)的零點(diǎn)1、函數(shù)零點(diǎn)的概念:對(duì)于函數(shù)SKIPIF1<0，把使SKIPIF1<0成立的實(shí)數(shù)SKIPIF1<0叫做函數(shù)SKIPIF1〈0的零點(diǎn)。2、函數(shù)零點(diǎn)的意義:函數(shù)SKIPIF1<0的零點(diǎn)就是方程SKIPIF1〈0實(shí)數(shù)根，亦即函數(shù)SKIPIF1<0的圖象與SKIPIF1〈0軸交點(diǎn)的橫坐標(biāo)。即：方程SKIPIF1〈0有實(shí)數(shù)根SKIPIF1〈0函數(shù)SKIPIF1〈0的圖象與SKIPIF1<0軸有交點(diǎn)SKIPIF1〈0函數(shù)SKIPIF1<0有零點(diǎn)．3、函數(shù)零點(diǎn)的求法：eq\o\ac（○，1）(代數(shù)法）求方程SKIPIF1〈0的實(shí)數(shù)根；eq\o\ac(○，2）（幾何法）對(duì)于不能用求根公式的方程，可以將它與函數(shù)SKIPIF1<0的圖象聯(lián)系起來(lái)，并利用函數(shù)的性質(zhì)找出零點(diǎn)．4、基本初等函數(shù)的零點(diǎn)：①正比例函數(shù)SKIPIF1<0僅有一個(gè)零點(diǎn)。②反比例函數(shù)SKIPIF1<0沒(méi)有零點(diǎn)。③一次函數(shù)SKIPIF1<0僅有一個(gè)零點(diǎn)。④二次函數(shù)SKIPIF1<0．（1）△＞０，方程SKIPIF1〈0有兩不等實(shí)根，二次函數(shù)的圖象與SKIPIF1〈0軸有兩個(gè)交點(diǎn)，二次函數(shù)有兩個(gè)零點(diǎn)．（2)△＝０，方程SKIPIF1<0有兩相等實(shí)根，二次函數(shù)的圖象與SKIPIF1<0軸有一個(gè)交點(diǎn)，二次函數(shù)有一個(gè)二重零點(diǎn)或二階零點(diǎn)．（3）△＜０，方程SKIPIF1〈0無(wú)實(shí)根，二次函數(shù)的圖象與SKIPIF1〈0軸無(wú)交點(diǎn),二次函數(shù)無(wú)零點(diǎn)．⑤指數(shù)函數(shù)SKIPIF1<0沒(méi)有零點(diǎn)。⑥對(duì)數(shù)函數(shù)SKIPIF1<0僅有一個(gè)零點(diǎn)1。⑦冪函數(shù)SKIPIF1〈0，當(dāng)SKIPIF1〈0時(shí)，僅有一個(gè)零點(diǎn)0，當(dāng)SKIPIF1<0時(shí),沒(méi)有零點(diǎn)。5、非基本初等函數(shù)(不可直接求出零點(diǎn)的較復(fù)雜的函數(shù)）,函數(shù)先把SKIPIF1<0轉(zhuǎn)化成SKIPIF1<0，再把復(fù)雜的函數(shù)拆分成兩個(gè)我們常見的函數(shù)SKIPIF1〈0（基本初等函數(shù)），這另個(gè)函數(shù)圖像的交點(diǎn)個(gè)數(shù)就是函數(shù)SKIPIF1<0零點(diǎn)的個(gè)數(shù)。即f（x)=g(x)的解集f(x)的圖像和g(x)的圖像的交點(diǎn)。6、選擇題判斷區(qū)間SKIPIF1〈0上是否含有零點(diǎn)，只需滿足SKIPIF1〈0。7、確定零點(diǎn)在某區(qū)間SKIPIF1<0個(gè)數(shù)是唯一的條件是：①SKIPIF1<0在區(qū)間上連續(xù)，且SKIPIF1<0②在區(qū)間SKIPIF1<0上單調(diào)。8、函數(shù)零點(diǎn)的性質(zhì):從“數(shù)"的角度看：即是使SKIPIF1<0的實(shí)數(shù)；從“形”的角度看:即是函數(shù)SKIPIF1<0的圖象與SKIPIF1<0軸交點(diǎn)的橫坐標(biāo);若函數(shù)SKIPIF1〈0的圖象在SKIPIF1<0處與SKIPIF1<0軸相切，則零點(diǎn)SKIPIF1〈0通常稱為不變號(hào)零點(diǎn)；若函數(shù)SKIPIF1<0的圖象在SKIPIF1<0處與SKIPIF1<0軸相交，則零點(diǎn)SKIPIF1〈0通常稱為變號(hào)零點(diǎn)．9、二分法的定義對(duì)于在區(qū)間SKIPIF1〈0，SKIPIF1〈0上連續(xù)不斷，且滿足SKIPIF1<0的函數(shù)SKIPIF1<0,通過(guò)不斷地把函數(shù)SKIPIF1〈0的零點(diǎn)所在的區(qū)間一分為二，使區(qū)間的兩個(gè)端點(diǎn)逐步逼近零點(diǎn),進(jìn)而得到零點(diǎn)近似值的方法叫做二分法．10、給定精確度ε，用二分法求函數(shù)SKIPIF1<0零點(diǎn)近似值的步驟：(1)確定區(qū)間SKIPIF1<0，SKIPIF1<0，驗(yàn)證SKIPIF1<0SKIPIF1〈0,給定精度SKIPIF1<0；(2）求區(qū)間SKIPIF1<0,SKIPIF1〈0的中點(diǎn)SKIPIF1<0；（3）計(jì)算SKIPIF1<0：①若SKIPIF1〈0=SKIPIF1〈0，則SKIPIF1<0就是函數(shù)的零點(diǎn)；②若SKIPIF1<0SKIPIF1<0SKIPIF1〈0<SKIPIF1〈0,則令SKIPIF1〈0=SKIPIF1<0（此時(shí)零點(diǎn)SKIPIF1<0）；③若SKIPIF1<0SKIPIF1〈0SKIPIF1〈0〈SKIPIF1<0，則令SKIPIF1〈0=SKIPIF1<0（此時(shí)零點(diǎn)SKIPIF1〈0）；（4)判斷是否達(dá)到精度SKIPIF1<0；即若SKIPIF1<0，則得到零點(diǎn)值SKIPIF1〈0(或SKIPIF1〈0）；否則重復(fù)步驟（2)-（4)．11、二分法的條件SKIPIF1<0·SKIPIF1<0SKIPIF1〈0表明用二分法求函數(shù)的近似零點(diǎn)都是指變號(hào)零點(diǎn)。12、解決應(yīng)用題的一般程序：①審題：弄清題意，分清條件和結(jié)論，理順數(shù)量關(guān)系;②建模:將文字語(yǔ)言轉(zhuǎn)化為數(shù)學(xué)語(yǔ)言,利用數(shù)學(xué)知識(shí),建立相應(yīng)的數(shù)學(xué)模型；③解模:求解數(shù)學(xué)模型，得出數(shù)學(xué)結(jié)論；④還原:將用數(shù)學(xué)知識(shí)和方法得出的結(jié)論，還原為實(shí)際問(wèn)題的意義．例題分析【例1】若方程SKIPIF1<0有4個(gè)不相等的實(shí)數(shù)根，則實(shí)數(shù)SKIPIF1<0的取值范圍是.【例2】若函數(shù)f（x）＝x2－(2a－4）x－3在[1，3]上的最小值是g（a），求g（a）的函數(shù)表達(dá)式．針對(duì)練習(xí)一、選擇題1．已知函數(shù)SKIPIF1〈0唯一的零點(diǎn)在區(qū)間SKIPIF1<0內(nèi),那么下面命題錯(cuò)誤的(） A函數(shù)SKIPIF1〈0在SKIPIF1〈0或SKIPIF1〈0內(nèi)有零點(diǎn)B函數(shù)SKIPIF1〈0在SKIPIF1〈0內(nèi)無(wú)零點(diǎn) C函數(shù)SKIPIF1〈0在SKIPIF1<0內(nèi)有零點(diǎn)Dhttp：///"SKIPIF1<0BHYPERLINK”http：///”SKIPIF1〈0CHYPERLINK”http：///"SKIPIF1〈0Dhttp：///"14.若方程SKIPIF1<0的實(shí)根在區(qū)間SKIPIF1〈0內(nèi)，且SKIPIF1<0，則SKIPIF1〈0.HYPERLINK”/”15。設(shè)y=f（x）的圖象在［a，b]上連續(xù),若滿足，則方程f（x）=0在[a，b]上有實(shí)根。三、解答題16、有一塊長(zhǎng)為20cm,寬為12cm的矩形鐵皮，將其四個(gè)角各截去一個(gè)邊長(zhǎng)為SKIPIF1〈0的小正方形，然后折成一個(gè)無(wú)蓋的盒子,寫出這個(gè)盒子的體積V與邊長(zhǎng)SKIPIF1<0的函數(shù)關(guān)系式，并討論這個(gè)函數(shù)的定義域。17。設(shè)SKIPIF1〈0與SKIPIF1<0分別是實(shí)系數(shù)方程SKIPIF1〈0和SKIPIF1〈0的一個(gè)根,且SKIPIF1<0，求證：方程SKIPIF1〈0有且僅有一根介于SKIPIF1<0和SKIPIF1〈0之間.18.已知函數(shù)f（x)=SKIPIF1<0（a，b為常數(shù)，且a≠0）滿足f(2）=1且方程f(x)=x有唯一解，求函數(shù)f（x)的解析式19．已知函數(shù)SKIPIF1〈0的定義域?yàn)椋?，+∞),且滿足對(duì)任意的SKIPIF1<0＞0，y＞0，SKIPIF1<0,SKIPIF1〈0.當(dāng)SKIPIF1〈0＞1時(shí)，SKIPIF1<0＞0.（1）求SKIPIF1〈0的值；(2）判斷SKIPIF1〈0的單調(diào)性，并加以證明；（3）解不等式SKIPIF1<0.三、布置作業(yè)1.方程SKIPIF1〈0的根所在的區(qū)間為（）A、SKIPIF1〈0B、SKIPIF