新高考數(shù)學(xué)二輪復(fù)習(xí)重難點(diǎn)突破專題13 利用導(dǎo)數(shù)證明或求函數(shù)的單調(diào)區(qū)間(原卷版)

專題13利用導(dǎo)數(shù)證明或求函數(shù)的單調(diào)區(qū)間一、多選題1．已知函數(shù)SKIPIF1<0，數(shù)列SKIPIF1<0的前n項(xiàng)和為SKIPIF1<0，且滿足SKIPIF1<0，SKIPIF1<0，則下列有關(guān)數(shù)列SKIPIF1<0的敘述正確的是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．設(shè)函數(shù)SKIPIF1<0的導(dǎo)函數(shù)為SKIPIF1<0，則（）A．SKIPIF1<0 B．SKIPIF1<0是SKIPIF1<0的極值點(diǎn)C．SKIPIF1<0存在零點(diǎn) D．SKIPIF1<0在SKIPIF1<0單調(diào)遞增3．已知函數(shù)SKIPIF1<0，SKIPIF1<0，則下列結(jié)論正確的有（）A．SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減B．若SKIPIF1<0，則SKIPIF1<0C．SKIPIF1<0在區(qū)間SKIPIF1<0上的值域?yàn)镾KIPIF1<0D．若函數(shù)SKIPIF1<0，且SKIPIF1<0，SKIPIF1<0在SKIPIF1<0上單調(diào)遞減4．已知函數(shù)SKIPIF1<0，給出下列四個(gè)結(jié)論，其中正確的是（）A．曲線SKIPIF1<0在SKIPIF1<0處的切線方程為SKIPIF1<0B．SKIPIF1<0恰有2個(gè)零點(diǎn)C．SKIPIF1<0既有最大值，又有最小值D．若SKIPIF1<0且SKIPIF1<0，則SKIPIF1<05．已知函數(shù)SKIPIF1<0，則下列說(shuō)法正確的是（）A．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0單調(diào)遞增B．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0處的切線為SKIPIF1<0軸C．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0在SKIPIF1<0存在唯一極小值點(diǎn)SKIPIF1<0，且SKIPIF1<0D．對(duì)任意SKIPIF1<0，SKIPIF1<0在SKIPIF1<0一定存在零點(diǎn)二、單選題6．已知定義域?yàn)镽的函數(shù)SKIPIF1<0的圖象連續(xù)不斷，且SKIPIF1<0，SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，若SKIPIF1<0，則實(shí)數(shù)m的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．函數(shù)SKIPIF1<0的圖象大致是（）A． B．C． D．8．設(shè)函數(shù)SKIPIF1<0在SKIPIF1<0上存在導(dǎo)數(shù)SKIPIF1<0，對(duì)于任意的實(shí)數(shù)SKIPIF1<0，有SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，若SKIPIF1<0，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．函數(shù)SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．已知函數(shù)SKIPIF1<0，則其單調(diào)增區(qū)間是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．某數(shù)學(xué)興趣小組對(duì)形如SKIPIF1<0的某三次函數(shù)的性質(zhì)進(jìn)行研究，得出如下四個(gè)結(jié)論，其中有且只有一個(gè)是錯(cuò)誤的，則錯(cuò)誤的結(jié)論一定是（）A．函數(shù)SKIPIF1<0的圖象過(guò)點(diǎn)(2，1)B．函數(shù)SKIPIF1<0在x＝0處有極值C．函數(shù)SKIPIF1<0的單調(diào)遞減區(qū)間為[0，2]D．函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)(1，0)對(duì)稱12．函數(shù)SKIPIF1<0的圖象大致是（）A． B．

C． D．

13．已知偶函數(shù)SKIPIF1<0對(duì)于任意的SKIPIF1<0滿足SKIPIF1<0（其中SKIPIF1<0是函數(shù)SKIPIF1<0的導(dǎo)函數(shù)），則下列不等式中成立的是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<014．已知函數(shù)SKIPIF1<0在定義域SKIPIF1<0上的導(dǎo)函數(shù)為SKIPIF1<0，若函數(shù)SKIPIF1<0沒(méi)有零點(diǎn)，且SKIPIF1<0SKIPIF1<0，當(dāng)SKIPIF1<0在SKIPIF1<0上與SKIPIF1<0在SKIPIF1<0上的單調(diào)性相同時(shí)，則實(shí)數(shù)k的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．函數(shù)y=f(x)的導(dǎo)函數(shù)y=f′(x)的圖象如圖所示，給出下列命題：①-3是函數(shù)y=f(x)的極值點(diǎn)；②y=f(x)在區(qū)間(-3，1)上單調(diào)遞增；③-1是函數(shù)y=f(x)的最小值點(diǎn)；④y=f(x)在x=0處切線的斜率小于零.以上正確命題的序號(hào)是（）A．①② B．③④ C．①③ D．②④16．已知f（x）是定義在R上的偶函數(shù)，且f（2）＝1，當(dāng)x＞0時(shí)，xf′（x）+f（x）＞1，則不等式SKIPIF1<0的解集為（）A．(-∞，2)∪(2，+∞) B．(-∞，2)∪(0，2)C．(-2，0)∪(2，+∞) D．(-2，0)∪(0，2)17．已知函數(shù)SKIPIF1<0，SKIPIF1<0，若對(duì)任意SKIPIF1<0，總存在SKIPIF1<0，使得SKIPIF1<0成立，則實(shí)數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<018．若定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則滿足SKIPIF1<0的值（）A．恒小于0 B．恒等于0 C．恒大于0 D．無(wú)法判斷19．下列區(qū)間是函數(shù)SKIPIF1<0的單調(diào)遞減區(qū)間的是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<020．已知SKIPIF1<0為偶函數(shù)，且SKIPIF1<0，令SKIPIF1<0，若SKIPIF1<0時(shí)，SKIPIF1<0，關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集為（）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<021．已知SKIPIF1<0，則函數(shù)SKIPIF1<0的單調(diào)減區(qū)間為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<022．若函數(shù)SKIPIF1<0在SKIPIF1<0上是單調(diào)函數(shù)，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<023．已知f(x)是定義在R上的連續(xù)函數(shù)，f′(x)是f(x)的導(dǎo)函數(shù)，且f(x)-f(-x)+4x=0.若當(dāng)x>0時(shí)，f′(x)>-2，則不等式f(x-2)-f(x)>4的解集為（）A．(-∞，-1) B．(-∞，1) C．(-1，+∞) D．(1，+∞)24．已知函數(shù)SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0三、解答題25．函數(shù)SKIPIF1<0.（1）當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0的單調(diào)區(qū)間；（2）當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0恒成立，求整數(shù)SKIPIF1<0的最大值.26．函數(shù)SKIPIF1<0.（1）當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0的單調(diào)區(qū)間；（2）當(dāng)SKIPIF1<0，SKIPIF1<0時(shí)，證明：SKIPIF1<0.27．函數(shù)SKIPIF1<0.（1）若SKIPIF1<0，求SKIPIF1<0的單調(diào)性；（2）當(dāng)SKIPIF1<0時(shí)，若函數(shù)SKIPIF1<0有兩個(gè)零點(diǎn)，求證：SKIPIF1<0.28．設(shè)SKIPIF1<0為實(shí)數(shù)，已知函數(shù)SKIPIF1<0.（1）當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0的單調(diào)區(qū)間；（2）當(dāng)SKIPIF1<0時(shí)，若SKIPIF1<0有兩個(gè)不同的零點(diǎn)，求SKIPIF1<0的取值范圍.29．已知函數(shù)SKIPIF1<0.（1）若a=-2，求函數(shù)f(x)的單調(diào)區(qū)間；（2）若函數(shù)f(x)有兩個(gè)極值點(diǎn)x1，x2，求證SKIPIF1<0.30．設(shè)函數(shù)SKIPIF1<0.（1）若SKIPIF1<0，求SKIPIF1<0的單調(diào)區(qū)間；（2）若SKIPIF1<0時(shí)SKIPIF1<0，求SKIPIF1<0的取值范圍.31．已知函數(shù)SKIPIF1<0.（1）求函數(shù)SKIPIF1<0的單調(diào)區(qū)間；（2）在平面直角坐標(biāo)系SKIPIF1<0中，直線SKIPIF1<0與曲線SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，設(shè)點(diǎn)SKIPIF1<0的橫坐標(biāo)為SKIPIF1<0，SKIPIF1<0的面積為SKIPIF1<0.（i）求證：SKIPIF1<0；（ii）當(dāng)SKIPIF1<0取得最小值時(shí)，求SKIPIF1<0的值.32．已知函數(shù)SKIPIF1<0.（1）求SKIPIF1<0在點(diǎn)SKIPIF1<0處的切線方程；（2）求SKIPIF1<0的單調(diào)區(qū)間；（3）若SKIPIF1<0的定義域?yàn)镾KIPIF1<0時(shí)，值域?yàn)镾KIPIF1<0，求SKIPIF1<0的最大值.33．如圖，點(diǎn)SKIPIF1<0為某沿海城市的高速公路出入口，直線SKIPIF1<0為海岸線，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0是以SKIPIF1<0為圓心，半徑為SKIPIF1<0的圓弧型小路.該市擬修建一條從SKIPIF1<0通往海岸的觀光專線SKIPIF1<0，其中SKIPIF1<0為SKIPIF1<0上異于SKIPIF1<0的一點(diǎn)，SKIPIF1<0與SKIPIF1<0平行，設(shè)SKIPIF1<0.（1）證明：觀光專線SKIPIF1<0的總長(zhǎng)度隨SKIPIF1<0的增大而減??；（2）已知新建道路SKIPIF1<0的單位成本是