(完整word版)(整理)函數(shù)應用零點二分法知識點和練習.(完整word版)(整理)函數(shù)應用零點二分法知識點和練習.精品文檔精品文檔(完整word版)(整理)函數(shù)應用零點二分法知識點和練習.精品文檔一、方程的根與函數(shù)的零點1、函數(shù)零點的概念:對于函數(shù)SKIPIF1<0，把使SKIPIF1<0成立的實數(shù)SKIPIF1<0叫做函數(shù)SKIPIF1〈0的零點。2、函數(shù)零點的意義:函數(shù)SKIPIF1<0的零點就是方程SKIPIF1〈0實數(shù)根，亦即函數(shù)SKIPIF1<0的圖象與SKIPIF1〈0軸交點的橫坐標。即：方程SKIPIF1〈0有實數(shù)根SKIPIF1〈0函數(shù)SKIPIF1〈0的圖象與SKIPIF1<0軸有交點SKIPIF1〈0函數(shù)SKIPIF1<0有零點．3、函數(shù)零點的求法：eq\o\ac（○，1）(代數(shù)法）求方程SKIPIF1〈0的實數(shù)根；eq\o\ac(○，2）（幾何法）對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，并利用函數(shù)的性質找出零點．4、基本初等函數(shù)的零點：①正比例函數(shù)SKIPIF1<0僅有一個零點。②反比例函數(shù)SKIPIF1<0沒有零點。③一次函數(shù)SKIPIF1<0僅有一個零點。④二次函數(shù)SKIPIF1<0．（1）△＞０，方程SKIPIF1〈0有兩不等實根，二次函數(shù)的圖象與SKIPIF1〈0軸有兩個交點，二次函數(shù)有兩個零點．（2)△＝０，方程SKIPIF1<0有兩相等實根，二次函數(shù)的圖象與SKIPIF1<0軸有一個交點，二次函數(shù)有一個二重零點或二階零點．（3）△＜０，方程SKIPIF1〈0無實根，二次函數(shù)的圖象與SKIPIF1〈0軸無交點,二次函數(shù)無零點．⑤指數(shù)函數(shù)SKIPIF1<0沒有零點。⑥對數(shù)函數(shù)SKIPIF1<0僅有一個零點1。⑦冪函數(shù)SKIPIF1〈0，當SKIPIF1〈0時，僅有一個零點0，當SKIPIF1<0時,沒有零點。5、非基本初等函數(shù)(不可直接求出零點的較復雜的函數(shù)）,函數(shù)先把SKIPIF1<0轉化成SKIPIF1<0，再把復雜的函數(shù)拆分成兩個我們常見的函數(shù)SKIPIF1〈0（基本初等函數(shù)），這另個函數(shù)圖像的交點個數(shù)就是函數(shù)SKIPIF1<0零點的個數(shù)。即f（x)=g(x)的解集f(x)的圖像和g(x)的圖像的交點。6、選擇題判斷區(qū)間SKIPIF1〈0上是否含有零點，只需滿足SKIPIF1〈0。7、確定零點在某區(qū)間SKIPIF1<0個數(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。8、函數(shù)零點的性質:從“數(shù)"的角度看：即是使SKIPIF1<0的實數(shù)；從“形”的角度看:即是函數(shù)SKIPIF1<0的圖象與SKIPIF1<0軸交點的橫坐標;若函數(shù)SKIPIF1〈0的圖象在SKIPIF1<0處與SKIPIF1<0軸相切，則零點SKIPIF1〈0通常稱為不變號零點；若函數(shù)SKIPIF1<0的圖象在SKIPIF1<0處與SKIPIF1<0軸相交，則零點SKIPIF1〈0通常稱為變號零點．9、二分法的定義對于在區(qū)間SKIPIF1〈0，SKIPIF1〈0上連續(xù)不斷，且滿足SKIPIF1<0的函數(shù)SKIPIF1<0,通過不斷地把函數(shù)SKIPIF1〈0的零點所在的區(qū)間一分為二，使區(qū)間的兩個端點逐步逼近零點,進而得到零點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<0零點近似值的步驟：(1)確定區(qū)間SKIPIF1<0，SKIPIF1<0，驗證SKIPIF1<0SKIPIF1〈0,給定精度SKIPIF1<0；(2）求區(qū)間SKIPIF1<0,SKIPIF1〈0的中點SKIPIF1<0；（3）計算SKIPIF1<0：①若SKIPIF1〈0=SKIPIF1〈0，則SKIPIF1<0就是函數(shù)的零點；②若SKIPIF1<0SKIPIF1<0SKIPIF1〈0<SKIPIF1〈0,則令SKIPIF1〈0=SKIPIF1<0（此時零點SKIPIF1<0）；③若SKIPIF1<0SKIPIF1〈0SKIPIF1〈0〈SKIPIF1<0，則令SKIPIF1〈0=SKIPIF1<0（此時零點SKIPIF1〈0）；（4)判斷是否達到精度SKIPIF1<0；即若SKIPIF1<0，則得到零點值SKIPIF1〈0(或SKIPIF1〈0）；否則重復步驟（2)-（4)．11、二分法的條件SKIPIF1<0·SKIPIF1<0SKIPIF1〈0表明用二分法求函數(shù)的近似零點都是指變號零點。12、解決應用題的一般程序：①審題：弄清題意，分清條件和結論，理順數(shù)量關系;②建模:將文字語言轉化為數(shù)學語言,利用數(shù)學知識,建立相應的數(shù)學模型；③解模:求解數(shù)學模型，得出數(shù)學結論；④還原:將用數(shù)學知識和方法得出的結論，還原為實際問題的意義．例題分析【例1】若方程SKIPIF1<0有4個不相等的實數(shù)根，則實數(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)表達式．針對練習一、選擇題1．已知函數(shù)SKIPIF1〈0唯一的零點在區(qū)間SKIPIF1<0內,那么下面命題錯誤的(） A函數(shù)SKIPIF1〈0在SKIPIF1〈0或SKIPIF1〈0內有零點B函數(shù)SKIPIF1〈0在SKIPIF1〈0內無零點 C函數(shù)SKIPIF1〈0在SKIPIF1<0內有零點Dhttp：///"SKIPIF1<0BHYPERLINK”http：///”SKIPIF1〈0CHYPERLINK”http：///"SKIPIF1〈0Dhttp：///"14.若方程SKIPIF1<0的實根在區(qū)間SKIPIF1〈0內，且SKIPIF1<0，則SKIPIF1〈0.HYPERLINK”/”15。設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]上有實根。三、解答題16、有一塊長為20cm,寬為12cm的矩形鐵皮，將其四個角各截去一個邊長為SKIPIF1〈0的小正方形，然后折成一個無蓋的盒子,寫出這個盒子的體積V與邊長SKIPIF1<0的函數(shù)關系式，并討論這個函數(shù)的定義域。17。設SKIPIF1〈0與SKIPIF1<0分別是實系數(shù)方程SKIPIF1〈0和SKIPIF1〈0的一個根,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的定義域為（0，+∞),且滿足對任意的SKIPIF1<0＞0，y＞0，SKIPIF1<0,SKIPIF1〈0.當SKIPIF1〈0＞1時，SKIPIF1<0＞0.（1）求SKIPIF1〈0的值；(2）判斷SKIPIF1〈0的單調性，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