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專(zhuān)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(méi)有極值,則實(shí)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(gè)不同的極值點(diǎn),則實(shí)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(gè)相鄰的極值點(diǎn),則SKIPIF1<0(
)A.3 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<05.已知SKIPIF1<0沒(méi)有極值,則實(shí)數(shù)SKIPIF1<0的取值范圍為(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<06.設(shè)函數(shù)f(x)=lnx+SKIPIF1<0在SKIPIF1<0內(nèi)有極值,求實(shí)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(duì)(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(diǎn),則實(shí)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(diǎn),則實(shí)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(gè)極值點(diǎn),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(gè)極值點(diǎn),則實(shí)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(gè)子區(qū)間SKIPIF1<0上有極值,則實(shí)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(gè)極值點(diǎn),其中一個(gè)極值點(diǎn)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(gè)極值點(diǎn)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(shí)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(gè)極值點(diǎn),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(gè)極值點(diǎn),則實(shí)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(shí)數(shù)SKIPIF1<0的值為_(kāi)_____.22.若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)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(diǎn),則a的取值范圍是______.24.設(shè)函數(shù)SKIPIF1<0,若SKIPIF1<0是函數(shù)SKIPIF1<0的一個(gè)極大值點(diǎn),則實(shí)數(shù)b的取值范圍為_(kāi)_________.25.已知函數(shù)SKIPIF1<0在SKIPIF1<0上恰有一個(gè)極值,則SKIPIF1<0___________.26.若函數(shù)SKIPIF1<0在SKIPIF1<0處取得極小值,則實(shí)數(shù)m的取值范圍為_(kāi)_____.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(diào)性.28.已知函數(shù)SKIPIF1<0(1)當(dāng)SKIPIF1<0,證明:SKIPIF1<0;(2)若函數(shù)SKIPIF1<0在SKIPIF1<0上恰有一個(gè)極值,求a的值.29.已知函數(shù)SKIPIF1<0.(1)當(dāng)SKIPIF1<0時(shí),證明:當(dāng)SKIPIF1<0時(shí),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(dāng)SKIPIF1<0時(shí),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(gè)不同的實(shí)數(shù)根,求實(shí)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(duì)數(shù)的底數(shù))(1)當(dāng)SKIPIF1<0時(shí),求函數(shù)SKIPIF1<0的單調(diào)區(qū)間;(2)當(dāng)SKIPIF1<0時(shí),若SKIPIF1<0是SKIPIF1<0的兩極值點(diǎn)且SKIPIF1<0,求實(shí)數(shù)a的取值范圍.32.設(shè)函數(shù)SKIPIF1<0.(1)若曲線SKIPIF1<0在點(diǎn)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(dāng)SKIPIF1<0時(shí),求函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間;(2)設(shè)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(diào)區(qū)間;(2)若SKIPIF1<0存在兩個(gè)極小值點(diǎn)SKIPIF1<0,求實(shí)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(diào)性;(2)若SKIPIF1<0有且只有一個(gè)極值點(diǎn),求a的取值范圍.36.已知函數(shù)SKIPIF1<0,曲線SKIPIF1<0在點(diǎn)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(duì)數(shù)的底數(shù).(1)求證:當(dāng)SKIPIF1<0時(shí),函數(shù)f(x)是減函數(shù);(2)若函數(shù)f(x)存在極值,求實(shí)數(shù)a的取值范圍.38.已知函數(shù)SKIPIF1<0,SKIPIF1<0,SKIPIF1<0.(
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