專題04構(gòu)造函數(shù)法解決不等式問(wèn)題(典型題型歸類訓(xùn)練)目錄TOC\o"1-2"\h\u一、必備秘籍 1二、典型題型 2題型一：構(gòu)造SKIPIF1<0或SKIPIF1<0(SKIPIF1<0，且SKIPIF1<0)型 2題型二：構(gòu)造SKIPIF1<0或SKIPIF1<0(SKIPIF1<0，且SKIPIF1<0)型 3題型三：構(gòu)造SKIPIF1<0或SKIPIF1<0型 4題型四：構(gòu)造SKIPIF1<0或SKIPIF1<0型 5三、專項(xiàng)訓(xùn)練 5一、必備秘籍1、兩個(gè)基本還原①SKIPIF1<0②SKIPIF1<02、類型一：構(gòu)造可導(dǎo)積函數(shù)①SKIPIF1<0高頻考點(diǎn)1：SKIPIF1<0②SKIPIF1<0高頻考點(diǎn)1：SKIPIF1<0高頻考點(diǎn)2SKIPIF1<0③SKIPIF1<0高頻考點(diǎn)1：SKIPIF1<0④SKIPIF1<0高頻考點(diǎn)1：SKIPIF1<0高頻考點(diǎn)2SKIPIF1<0⑤SKIPIF1<0⑥SKIPIF1<0序號(hào)條件構(gòu)造函數(shù)1SKIPIF1<0SKIPIF1<02SKIPIF1<0SKIPIF1<03SKIPIF1<0SKIPIF1<04SKIPIF1<0SKIPIF1<05SKIPIF1<0SKIPIF1<06SKIPIF1<0SKIPIF1<07SKIPIF1<0SKIPIF1<08SKIPIF1<0SKIPIF1<03、類型二：構(gòu)造可商函數(shù)①SKIPIF1<0高頻考點(diǎn)1：SKIPIF1<0②SKIPIF1<0高頻考點(diǎn)1：SKIPIF1<0高頻考點(diǎn)2：SKIPIF1<0③SKIPIF1<0⑥SKIPIF1<0二、典型題型題型一：構(gòu)造SKIPIF1<0或SKIPIF1<0(SKIPIF1<0，且SKIPIF1<0)型1．（2023下·重慶榮昌·高二重慶市榮昌中學(xué)校?？计谥校┒x在SKIPIF1<0上的偶函數(shù)SKIPIF1<0的導(dǎo)函數(shù)為SKIPIF1<0，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0．則（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2023下·四川綿陽(yáng)·高二鹽亭中學(xué)?？茧A段練習(xí)）若函數(shù)SKIPIF1<0滿足SKIPIF1<0在SKIPIF1<0上恒成立，且SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2023下·陜西咸陽(yáng)·高二統(tǒng)考期中）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0，其導(dǎo)函數(shù)為SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的大小關(guān)系是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2023·甘肅張掖·甘肅省民樂(lè)縣第一中學(xué)?？寄M預(yù)測(cè)）已知SKIPIF1<0為偶函數(shù)，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，其中SKIPIF1<0為SKIPIF1<0的導(dǎo)數(shù)，則不等式SKIPIF1<0的解集為．5．（2023上·黑龍江·高三黑龍江實(shí)驗(yàn)中學(xué)校考階段練習(xí)）已知SKIPIF1<0是定義域?yàn)镾KIPIF1<0的偶函數(shù)，且SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則使得SKIPIF1<0成立的SKIPIF1<0的取值范圍是.題型二：構(gòu)造SKIPIF1<0或SKIPIF1<0(SKIPIF1<0，且SKIPIF1<0)型1．（2023上·福建莆田·高三莆田一中?？计谥校┮阎x域?yàn)镽的函數(shù)SKIPIF1<0，其導(dǎo)函數(shù)為SKIPIF1<0，且滿足SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<02．（2023上·四川內(nèi)江·高三期末）已知SKIPIF1<0是函數(shù)SKIPIF1<0的導(dǎo)函數(shù)，SKIPIF1<0，其中SKIPIF1<0是自然對(duì)數(shù)的底數(shù)，對(duì)任意SKIPIF1<0，恒有SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023下·河南洛陽(yáng)·高二統(tǒng)考期末）已知SKIPIF1<0是定義在R上的函數(shù)SKIPIF1<0的導(dǎo)函數(shù)，對(duì)于任意的實(shí)數(shù)x，都有SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0．若SKIPIF1<0，則實(shí)數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2023上·新疆伊犁·高三奎屯市第一高級(jí)中學(xué)?？茧A段練習(xí)）定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，且有SKIPIF1<0，則SKIPIF1<0的解集為.5．（2018上·江西贛州·高三統(tǒng)考期中）函數(shù)SKIPIF1<0的定義域和值域均為SKIPIF1<0，SKIPIF1<0的導(dǎo)函數(shù)為SKIPIF1<0，且滿足SKIPIF1<0，則SKIPIF1<0的取值范圍是．題型三：構(gòu)造SKIPIF1<0或SKIPIF1<0型1．（2023下·四川成都·高二期末）記函數(shù)SKIPIF1<0的導(dǎo)函數(shù)為SKIPIF1<0，若SKIPIF1<0為奇函數(shù)，且當(dāng)SKIPIF1<0時(shí)恒有SKIPIF1<0成立，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2023·青海海東·統(tǒng)考模擬預(yù)測(cè)）已知SKIPIF1<0是奇函數(shù)SKIPIF1<0的導(dǎo)函數(shù)，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2023上·云南昆明·高三昆明一中校考階段練習(xí)）定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0的導(dǎo)函數(shù)為SKIPIF1<0，且當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則不等式SKIPIF1<0的解集為．題型四：構(gòu)造SKIPIF1<0或SKIPIF1<0型1．（2023·全國(guó)·模擬預(yù)測(cè)）已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，不等式SKIPIF1<0恒成立（SKIPIF1<0為SKIPIF1<0的導(dǎo)函數(shù)），若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023下·山東聊城·高二?？茧A段練習(xí)）定義在SKIPIF1<0上的函數(shù)SKIPIF1<0，已知SKIPIF1<0是它的導(dǎo)函數(shù)，且恒有SKIPIF1<0成立，則有（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0三、專項(xiàng)訓(xùn)練一、單選題1．（2023上·上海徐匯·高三上海市第二中學(xué)?？计谥校┮阎x在R上的函數(shù)SKIPIF1<0，其導(dǎo)函數(shù)SKIPIF1<0滿足：對(duì)任意SKIPIF1<0都有SKIPIF1<0，則下列各式恒成立的是（

）A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<02．（2023·河南開(kāi)封·統(tǒng)考三模）設(shè)定義在SKIPIF1<0上的函數(shù)SKIPIF1<0的導(dǎo)函數(shù)SKIPIF1<0，且滿足SKIPIF1<0，SKIPIF1<0．則SKIPIF1<0、SKIPIF1<0、SKIPIF1<0的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2023下·云南保山·高二統(tǒng)考期末）已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，且當(dāng)SKIPIF1<0時(shí)不等式SKIPIF1<0成立，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0，SKIPIF1<0，SKIPIF1<0的大小關(guān)系是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2023·全國(guó)·高三專題練習(xí)）若函數(shù)SKIPIF1<0在R上可導(dǎo)，且滿足SKIPIF1<0恒成立，常數(shù)SKIPIF1<0則下列不等式一定成立的是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2023·全國(guó)·高三對(duì)口高考）已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的奇函數(shù)，且當(dāng)SKIPIF1<0時(shí)不等式SKIPIF1<0成立，若SKIPIF1<0，則SKIPIF1<0的大小關(guān)系是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2023·全國(guó)·高三對(duì)口高考）已知SKIPIF1<0是定義在SKIPIF1<0上的非負(fù)可導(dǎo)函數(shù)，且滿足SKIPIF1<0，對(duì)任意正數(shù)a、b，若SKIPIF1<0，則必有（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．（2023·云南·校聯(lián)考三模）設(shè)函數(shù)SKIPIF1<0在SKIPIF1<0上的導(dǎo)數(shù)存在，且SKIPIF1<0，則當(dāng)SKIPIF1<0時(shí)，（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<08．（2023下·湖北·高二校聯(lián)考期中）已知函數(shù)SKIPIF1<0的定義域?yàn)镽，SKIPIF1<0為SKIPIF1<0的導(dǎo)函數(shù)，且SKIPIF1<0，則不等式SKIPIF1<0的解集是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．（2023下·湖北武漢·高二武漢市洪山高級(jí)中學(xué)校聯(lián)考期中）設(shè)函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，SKIPIF1<0是其導(dǎo)函數(shù)，若SKIPIF1<0，SKIPIF1<0，則不等式SKIPIF1<0的解集是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2023下·湖北武漢·高二華中師大一附中?？计谥校㏒KIPIF1<0是定義在R上的奇函數(shù)，當(dāng)SKIPIF1<0時(shí)，有SKIPIF1<0恒成立，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<011．（2023下·河北張家口·高二校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0在SKIPIF1<0上連續(xù)且可導(dǎo)，同時(shí)滿足SKIPIF1<0，則下列不等式一定成立的為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、填空題12．（2023上·河南焦作·高三統(tǒng)考開(kāi)學(xué)考試）已知定義在R上的函數(shù)SKIPIF1<0及其導(dǎo)函數(shù)SKIPIF1<0滿足SKIPIF1<0，若SKIPIF1<0，則滿足不等式SKIPIF1<0的x的取值范圍是．13．（2023下·湖北咸寧·高二鄂南高中?？茧A段練習(xí)）已知偶函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的可導(dǎo)函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0且SKIPIF1<0，則SKIPIF1<0的解集為.14．（2021下·江蘇鎮(zhèn)江·高一江蘇省丹陽(yáng)高級(jí)中學(xué)?？计谥校┖瘮?shù)SKIPIF1<0定義域?yàn)镾KIPIF1<0，其導(dǎo)函數(shù)是SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，有SKIPIF1<0，則關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集為．15．（2022下·江蘇·高二校聯(lián)考階段練習(xí)）函數(shù)SKIPIF1<0的定義域是SKIPIF1<0，其導(dǎo)函數(shù)是SKIPIF1<0，若SKIPIF1<0，則關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集為．16．（2021下·重慶江津·高二?？计谥校┮阎x在SKIPIF1<0上的偶函數(shù)SKIPIF1<0的導(dǎo)函數(shù)為SKIPIF1<0，當(dāng)SKIPIF1<0時(shí)，有SKIPIF1<0，且SKIPIF1<0，則使得SKIPIF1<0成立的SKIPIF1<0的取值范圍是.17．（2021下·山東濟(jì)南·高二山東師范大學(xué)附中校考期中）設(shè)