專題16利用導(dǎo)數(shù)研究雙變量問題破解雙參數(shù)不等式的方法：一是轉(zhuǎn)化，即由已知條件入手，尋找雙參數(shù)滿足的關(guān)系式，并把含雙參數(shù)的不等式轉(zhuǎn)化為含單參數(shù)的不等式；二是巧構(gòu)函數(shù)，再借用導(dǎo)數(shù)，判斷函數(shù)的單調(diào)性，從而求其最值；三是回歸雙參的不等式的證明，把所求的最值應(yīng)用到雙參不等式，即可證得結(jié)果.一、單選題1．已知SKIPIF1<0若對于任意兩個不等的正實數(shù)SKIPIF1<0、SKIPIF1<0，都有SKIPIF1<0恒成立，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知函數(shù)SKIPIF1<0，若SKIPIF1<0且滿足SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知函數(shù)SKIPIF1<0，且SKIPIF1<0有兩個極值點SKIPIF1<0，其中SKIPIF1<0，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．設(shè)函數(shù)SKIPIF1<0，函數(shù)SKIPIF1<0，若對于SKIPIF1<0，SKIPIF1<0，使SKIPIF1<0成立，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知e為自然對數(shù)的底數(shù)，若對任意SKIPIF1<0，總存在唯一的SKIPIF1<0，使得SKIPIF1<0，成立，則實數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．若函數(shù)SKIPIF1<0存在兩個極值點SKIPIF1<0和SKIPIF1<0，則SKIPIF1<0取值范圍為（

）A．(-∞，SKIPIF1<0] B．(-∞，SKIPIF1<0) C．(SKIPIF1<0，+∞) D．[SKIPIF1<0，+∞)7．已知SKIPIF1<0，且SKIPIF1<0，其中e為自然對數(shù)的底數(shù)，則下列選項中一定成立的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知在函數(shù)SKIPIF1<0，SKIPIF1<0，若對SKIPIF1<0，SKIPIF1<0恒成立，則實數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．已知函數(shù)SKIPIF1<0，SKIPIF1<0，曲線SKIPIF1<0上總存在兩點SKIPIF1<0，SKIPIF1<0，使曲線SKIPIF1<0在SKIPIF1<0兩點處的切線互相平行，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．已知SKIPIF1<0，其中a≠b，若SKIPIF1<0恒成立，則實數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．已知函數(shù)SKIPIF1<0，若SKIPIF1<0有兩個零點SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題12．已知函數(shù)SKIPIF1<0和SKIPIF1<0，若SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<013．已知函數(shù)SKIPIF1<0，SKIPIF1<0，若對任意的SKIPIF1<0，均存在SKIPIF1<0，使得SKIPIF1<0，則a的取值可能是（

）A．0 B．2 C．SKIPIF1<0 D．114．已知函數(shù)SKIPIF1<0有兩個極值點SKIPIF1<0，SKIPIF1<0，則（

）A．a(chǎn)的取值范圍為（－∞，1） B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<015．已知SKIPIF1<0為常數(shù)，函數(shù)SKIPIF1<0有兩個極值點SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<016．已知函數(shù)SKIPIF1<0有兩個零點SKIPIF1<0，則（

）A．SKIPIF1<0的取值范圍為SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0三、填空題17．已知函數(shù)SKIPIF1<0，若存在SKIPIF1<0，使得SKIPIF1<0，則SKIPIF1<0的最小值為__________.18．已知SKIPIF1<0，SKIPIF1<0，若對SKIPIF1<0，SKIPIF1<0，使得SKIPIF1<0成立，則a的取值范圍是______．19．若函數(shù)SKIPIF1<0存在兩個極值點SKIPIF1<0和SKIPIF1<0，則SKIPIF1<0取值范圍為____.20．已知函數(shù)SKIPIF1<0，SKIPIF1<0，若對任意的SKIPIF1<0，總存在SKIPIF1<0，使得SKIPIF1<0成立，則實數(shù)a的取值范圍是_____．四、解答題21．已知函數(shù)SKIPIF1<0．(1)若SKIPIF1<0時，SKIPIF1<0，求a的取值范圍；(2)當(dāng)SKIPIF1<0時，方程SKIPIF1<0有兩個不相等的實數(shù)根SKIPIF1<0，SKIPIF1<0，證明：SKIPIF1<0．22．已知函數(shù)SKIPIF1<0，SKIPIF1<0.(1)討論SKIPIF1<0的單調(diào)性；(2)任取兩個正數(shù)SKIPIF1<0，當(dāng)SKIPIF1<0時，求證：SKIPIF1<0.23．已知函數(shù)SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）.(1)求函數(shù)SKIPIF1<0的極值；(2)若函數(shù)SKIPIF1<0的最小值為0，SKIPIF1<0，SKIPIF1<0（SKIPIF1<0）為函數(shù)SKIPIF1<0的兩個零點，證明：SKIPIF1<0.24．設(shè)函數(shù)SKIPIF1<0.(1)討論函數(shù)SKIPIF1<0的單調(diào)性；(2)若SKIPIF1<0有兩個零點SKIPIF1<0，①求a的取值范圍；②證明：SKIPIF1<0.25．已知函數(shù)SKIPIF1<0(1)當(dāng)SKIPIF1<0，研究SKIPIF1<0的單調(diào)性；(2)令SKIPIF1<0，若存在SKIPIF1<0使得SKIPIF1<0，求證SKIPIF1<0.26．已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0(1)若SKIPIF1<0恒成立，求SKIPIF1<0的最大值(2)若SKIPIF1<0，SKIPIF1<0是SKIPIF1<0的兩個零點，且SKIPIF1<0求證：SKIPIF1<027．已知函數(shù)SKIPIF1<0.(1)求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；(2)設(shè)SKIPIF1<0存在兩個極值點SKIPIF1<0，且SKIPIF1<0，若SKIPIF1<0，求證：SKIPIF1<0.28．設(shè)函數(shù)SKIPIF1<0，SKIPIF1<0