專題05利用函數(shù)極值求參(取值范圍)一、單選題1．函數(shù)SKIPIF1<0在SKIPIF1<0處有極大值SKIPIF1<0，則SKIPIF1<0的值等于（

）A．0 B．6 C．3 D．22．已知f(x)＝SKIPIF1<0x3＋(a－1)x2＋x＋1沒有極值，則實數(shù)a的取值范圍是（

）A．[0，1] B．(－∞，0]∪[1，＋∞)C．[0，2] D．(－∞，0]∪[2，＋∞)3．若函數(shù)SKIPIF1<0有兩個不同的極值點，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．若SKIPIF1<0，SKIPIF1<0是函數(shù)SKIPIF1<0SKIPIF1<0兩個相鄰的極值點，則SKIPIF1<0（

）A．3 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知SKIPIF1<0沒有極值，則實數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．設函數(shù)f(x)＝lnx＋SKIPIF1<0在SKIPIF1<0內有極值，求實數(shù)a的取值范圍（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知函數(shù)f(x)＝x3＋ax2＋bx＋a2在x＝1處的極值為10，則數(shù)對(a，b)為（

）A．(－3,3) B．(－11,4)C．(4，－11) D．(－3,3)或(4，－11)8．已知函數(shù)SKIPIF1<0，若SKIPIF1<0是SKIPIF1<0的極小值點，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．若函數(shù)SKIPIF1<0在R上有小于0的極值點，則實數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0有且僅有2個極值點，則m的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<011．已知函數(shù)SKIPIF1<0SKIPIF1<0有兩個極值點，則實數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．已知函數(shù)SKIPIF1<0在其定義域的一個子區(qū)間SKIPIF1<0上有極值，則實數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．已知函數(shù)SKIPIF1<0在SKIPIF1<0處取極小值，且SKIPIF1<0的極大值為4，則SKIPIF1<0（

）A．-1 B．2 C．-3 D．414．已知SKIPIF1<0為常數(shù)，函數(shù)SKIPIF1<0有兩個極值點，其中一個極值點SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．已知函數(shù)SKIPIF1<0有兩個極值點m，n，且SKIPIF1<0，則SKIPIF1<0的最大值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題16．已知函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0在SKIPIF1<0上有極值，則實數(shù)SKIPIF1<0可以?。?/p>

）A．1 B．2 C．3 D．417．函數(shù)SKIPIF1<0在SKIPIF1<0處取得極大值，則a的值可以是（

）A．-1 B．0 C．3 D．4三、填空題18．已知函數(shù)SKIPIF1<0在SKIPIF1<0處取得極值，則a＝______.19．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上恰有一個極值點，則SKIPIF1<0的取值范圍是___________.20．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上有兩個極值點，則實數(shù)a的取值范圍是______．21．已知函數(shù)SKIPIF1<0（SKIPIF1<0）在SKIPIF1<0處有極大值，則實數(shù)SKIPIF1<0的值為______．22．若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內存在極小值，則SKIPIF1<0的取值范圍是___________.23．函數(shù)SKIPIF1<0在SKIPIF1<0上存在極值點，則a的取值范圍是______．24．設函數(shù)SKIPIF1<0，若SKIPIF1<0是函數(shù)SKIPIF1<0的一個極大值點，則實數(shù)b的取值范圍為__________．25．已知函數(shù)SKIPIF1<0在SKIPIF1<0上恰有一個極值，則SKIPIF1<0___________.26．若函數(shù)SKIPIF1<0在SKIPIF1<0處取得極小值，則實數(shù)m的取值范圍為______．四、解答題27．已知定義在R上的函數(shù)SKIPIF1<0SKIPIF1<0，在SKIPIF1<0處取得極值.(1)求SKIPIF1<0的解析式；(2)討論SKIPIF1<0在區(qū)間SKIPIF1<0上的單調性.28．已知函數(shù)SKIPIF1<0(1)當SKIPIF1<0，證明：SKIPIF1<0；(2)若函數(shù)SKIPIF1<0在SKIPIF1<0上恰有一個極值，求a的值．29．已知函數(shù)SKIPIF1<0．(1)當SKIPIF1<0時，證明：當SKIPIF1<0時，SKIPIF1<0；(2)若SKIPIF1<0，函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上存在極大值，求a的取值范圍．30．若函數(shù)SKIPIF1<0，當SKIPIF1<0時，函數(shù)SKIPIF1<0取得極值SKIPIF1<0.(1)求函數(shù)SKIPIF1<0的解析式；(2)若方程SKIPIF1<0有3個不同的實數(shù)根，求實數(shù)k的取值范圍.31．已知函數(shù)SKIPIF1<0（其中SKIPIF1<0，SKIPIF1<0…為自然對數(shù)的底數(shù)）(1)當SKIPIF1<0時，求函數(shù)SKIPIF1<0的單調區(qū)間；(2)當SKIPIF1<0時，若SKIPIF1<0是SKIPIF1<0的兩極值點且SKIPIF1<0，求實數(shù)a的取值范圍．32．設函數(shù)SKIPIF1<0.(1)若曲線SKIPIF1<0在點SKIPIF1<0處的切線與SKIPIF1<0軸平行，求SKIPIF1<0；(2)若SKIPIF1<0在SKIPIF1<0處取得極大值，求SKIPIF1<0的取值范圍.33．已知函數(shù)SKIPIF1<0.(1)當SKIPIF1<0時，求函數(shù)SKIPIF1<0的單調遞增區(qū)間；(2)設函數(shù)SKIPIF1<0，若SKIPIF1<0在SKIPIF1<0上存在極值，求a的取值范圍.34．已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0，求函數(shù)SKIPIF1<0的單調區(qū)間；(2)若SKIPIF1<0存在兩個極小值點SKIPIF1<0，求實數(shù)SKIPIF1<0的取值范圍.35．已知函數(shù)SKIPIF1<0，SKIPIF1<0．(1)討論函數(shù)SKIPIF1<0的單調性；(2)若SKIPIF1<0有且只有一個極值點，求a的取值范圍．36．已知函數(shù)SKIPIF1<0，曲線SKIPIF1<0在點SKIPIF1<0處的切線斜率為0．(1)求b的值；(2)若函數(shù)SKIPIF1<0的極大值為SKIPIF1<0，證明：SKIPIF1<0．37．已知函數(shù)f(x)＝ax2＋xlnx－ex，其中e是自然對數(shù)的底數(shù)．(1)求證：當SKIPIF1<0時，函數(shù)f(x)是減函數(shù)；(2)若函數(shù)f(x)存在極值，求實數(shù)a的取值范圍．38．已知函數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0．(