函數(shù)、導數(shù)綜合復習練習題

..《函數(shù)》、《導數(shù)》綜合復習練習題1、已知函數(shù)SKIPIF1<0<Ⅰ>求函數(shù)SKIPIF1<0的單調(diào)區(qū)間;<Ⅱ>若集合SKIPIF1<0有且只有一個元素.求正數(shù)SKIPIF1<0的取值范圍．2、已知函數(shù)SKIPIF1<0SKIPIF1<0,SKIPIF1<0,記SKIPIF1<0〔Ⅰ求SKIPIF1<0的單調(diào)區(qū)間；〔Ⅱ當SKIPIF1<0時,若SKIPIF1<0,比較：SKIPIF1<0與SKIPIF1<0的大小；〔Ⅲ若SKIPIF1<0的極值為SKIPIF1<0,問是否存在實數(shù)SKIPIF1<0,使方程SKIPIF1<0有四個不同實數(shù)根？若存在,求出實數(shù)SKIPIF1<0的取值范圍；若不存在,請說明理由。3、已知函數(shù)SKIPIF1<0在x＝－SKIPIF1<0與x＝1時都取得極值．<Ⅰ>求SKIPIF1<0、b的值與函數(shù)SKIPIF1<0的單調(diào)遞減區(qū)間；<Ⅱ>若對SKIPIF1<0,不等式SKIPIF1<0恒成立,求c的取值范圍．4、設函數(shù)SKIPIF1<0.若SKIPIF1<0,求SKIPIF1<0的最小值；若當SKIPIF1<0時SKIPIF1<0,求實數(shù)SKIPIF1<0的取值范圍.5、已知函數(shù)SKIPIF1<0?！睮若SKIPIF1<0,求SKIPIF1<0的單調(diào)區(qū)間；<II>已知SKIPIF1<0是SKIPIF1<0的兩個不同的極值點,且SKIPIF1<0,若SKIPIF1<0恒成立,求實數(shù)b的取值范圍。6、已知函數(shù).〔1當時,求的單調(diào)區(qū)間；〔2若在單調(diào)增加,在單調(diào)減少,證明：＜6.7、已知函數(shù)SKIPIF1<0．〔1當SKIPIF1<0時,求SKIPIF1<0的最大值；〔2求證：SKIPIF1<0〔3對SKIPIF1<0圖象上的任意不同兩點SKIPIF1<0,證明SKIPIF1<0圖象上存在點SKIPIF1<0,且SKIPIF1<0圖象上以P0為切點的切線與直線P1P2平行．8、已知函數(shù),函數(shù)是區(qū)間[SKIPIF1<0,SKIPIF1<0]上的減函數(shù)．〔I求的最大值；〔II若上恒成立,求t的取值范圍；〔Ⅲ討論關于x的方程的根的個數(shù)．9、已知函數(shù)SKIPIF1<0在點SKIPIF1<0處的切線方程為SKIPIF1<0．〔1求SKIPIF1<0的值；〔2求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；〔3若方程SKIPIF1<0=m恰有兩個不等的實根,求m的取值范圍．10、已知函數(shù)g<x>=SKIPIF1<0在SKIPIF1<0上為增函數(shù),且SKIPIF1<0,f<x>=mx-SKIPIF1<0〔1求SKIPIF1<0的值；〔2若f<x>-g<x>在SKIPIF1<0上為單調(diào)函數(shù),求m的取值范圍；〔3設SKIPIF1<0,若在SKIPIF1<0上至少存在一個SKIPIF1<0,使得SKIPIF1<0成立,求m的取值范圍。11、若函數(shù)SKIPIF1<0在點SKIPIF1<0處的切線方程為SKIPIF1<0〔1求SKIPIF1<0的值；〔2求SKIPIF1<0的單調(diào)遞增區(qū)間；〔3若對于任意的SKIPIF1<0,恒有SKIPIF1<0成立,求實數(shù)SKIPIF1<0的取值范圍12、設函數(shù)SKIPIF1<0SKIPIF1<0〔1若SKIPIF1<0時函數(shù)SKIPIF1<0有三個互不相同的零點,求SKIPIF1<0的范圍；〔2若函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)沒有極值點,求SKIPIF1<0的范圍；〔3若對任意的SKIPIF1<0,不等式SKIPIF1<0在SKIPIF1<0上恒成立,求實數(shù)SKIPIF1<0的取值范圍.13、已知函數(shù)SKIPIF1<0．〔1若SKIPIF1<0在SKIPIF1<0時,有極值SKIPIF1<0,求SKIPIF1<0、SKIPIF1<0的值．〔2當SKIPIF1<0為非零實數(shù)時,SKIPIF1<0是否存在與直線SKIPIF1<0平行的切線,如果存在,求出切線的方程,如果不存在,說明理由．〔3設函數(shù)SKIPIF1<0的導函數(shù)為SKIPIF1<0,記函數(shù)SKIPIF1<0的最大值為M,求證SKIPIF1<0．14、設函數(shù)SKIPIF1<0,其中SKIPIF1<0為實常數(shù).〔Ⅰ當SKIPIF1<0為何值時,SKIPIF1<0；〔Ⅱ證明:當SKIPIF1<0時,函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)有兩個零點.15、已知函數(shù)SKIPIF1<0SKIPIF1<0?！?求函數(shù)SKIPIF1<0的極值；〔2若對任意的SKIPIF1<0都有SKIPIF1<0,求實數(shù)SKIPIF1<0的取值范圍.16、已知函數(shù)SKIPIF1<0,SKIPIF1<0〔1求SKIPIF1<0的極值；〔2若關于x的不等式SKIPIF1<0在SKIPIF1<0上恒成立,求k的取值范圍；〔3證明：SKIPIF1<0.18、已知函數(shù)SKIPIF1<0,SKIPIF1<0〔Ⅰ求SKIPIF1<0的單調(diào)區(qū)間和值域；〔Ⅱ設SKIPIF1<0,函數(shù)SKIPIF1<0,若對于任意SKIPIF1<0,總存在SKIPIF1<0,使得SKIPIF1<0成立,求SKIPIF1<0的取值范圍19、已知點ASKIPIF1<0在函數(shù)SKIPIF1<0的曲線上,而且以A點為切點的切線方程為：SK