新高考數(shù)學(xué)二輪復(fù)習(xí)解答題培優(yōu)練習(xí)專題02 利用導(dǎo)函數(shù)研究函數(shù)的單調(diào)性問題（常規(guī)問題）(典型題型歸類訓(xùn)練) 原卷版

專題02利用導(dǎo)函數(shù)研究函數(shù)的單調(diào)性問題（常規(guī)問題）(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：求已知函數(shù)（不含參）的單調(diào)區(qū)間 2題型二：已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)求參數(shù) 2題型三：已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上存在單調(diào)區(qū)間求參數(shù) 3題型四：已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上不單調(diào)求參數(shù) 4題型五：已知函數(shù)SKIPIF1<0在單調(diào)區(qū)間的個數(shù) 4三、專項訓(xùn)練 4一、必備秘籍1、求已知函數(shù)（不含參）的單調(diào)區(qū)間①求SKIPIF1<0的定義域②求SKIPIF1<0③令SKIPIF1<0，解不等式，求單調(diào)增區(qū)間④令SKIPIF1<0，解不等式，求單調(diào)減區(qū)間注：求單調(diào)區(qū)間時，令SKIPIF1<0（或SKIPIF1<0）不跟等號.2、已知函數(shù)SKIPIF1<0的遞增（遞減）區(qū)間為SKIPIF1<0SKIPIF1<0SKIPIF1<0，SKIPIF1<0是SKIPIF1<0的兩個根3、已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)①已知SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增SKIPIF1<0SKIPIF1<0，SKIPIF1<0恒成立.②已知SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減SKIPIF1<0SKIPIF1<0，SKIPIF1<0恒成立.注：已知單調(diào)性，等價條件中的不等式含等號.4、已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上存在單調(diào)區(qū)間①已知SKIPIF1<0在區(qū)間SKIPIF1<0上存在單調(diào)遞增區(qū)間SKIPIF1<0SKIPIF1<0，SKIPIF1<0有解.②已知SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞區(qū)間減SKIPIF1<0SKIPIF1<0，SKIPIF1<0有解.5、已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上不單調(diào)SKIPIF1<0SKIPIF1<0，使得SKIPIF1<0（且SKIPIF1<0是變號零點）二、典型題型題型一：求已知函數(shù)（不含參）的單調(diào)區(qū)間1．（2023上·河南·高三滎陽市高級中學(xué)校聯(lián)考階段練習(xí)）函數(shù)SKIPIF1<0的單調(diào)遞減區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023下·陜西漢中·高二校考期中）函數(shù)SKIPIF1<0的單調(diào)遞減區(qū)間為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023下·陜西寶雞·高二統(tǒng)考期末）函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間是（

）A．SKIPIF1<0和SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0和SKIPIF1<04．（2023·全國·高三專題練習(xí)）已知SKIPIF1<0，求SKIPIF1<0的單調(diào)性.題型二：已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)求參數(shù)1．（2023上·廣東汕頭·高三統(tǒng)考期中）設(shè)SKIPIF1<0，若函數(shù)SKIPIF1<0在SKIPIF1<0遞增，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023上·山西晉中·高三校考階段練習(xí)）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0單調(diào)遞增，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2023上·河南·高三校聯(lián)考階段練習(xí)）若函數(shù)SKIPIF1<0的圖象在區(qū)間SKIPIF1<0上單調(diào)遞增，則實數(shù)SKIPIF1<0的最小值為．4．（2023上·安徽亳州·高三蒙城縣第六中學(xué)?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則a的取值范圍是：.5．（2023下·高二課時練習(xí)）已知函數(shù)SKIPIF1<0是區(qū)間SKIPIF1<0上的單調(diào)函數(shù)，則SKIPIF1<0的取值范圍是．題型三：已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上存在單調(diào)區(qū)間求參數(shù)1．（2019下·安徽六安·高二校聯(lián)考期末）若函數(shù)SKIPIF1<0存在增區(qū)間，則實數(shù)SKIPIF1<0的取值范圍為A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2023下·江西撫州·高二江西省臨川第二中學(xué)?？茧A段練習(xí)）函數(shù)SKIPIF1<0在SKIPIF1<0上存在單調(diào)遞增區(qū)間，則SKIPIF1<0的取值范圍是.3．（2020上·北京·高三北師大二附中?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0在SKIPIF1<0上有增區(qū)間，則a的取值范圍是.4．（2019下·遼寧沈陽·高二校聯(lián)考期中）設(shè)SKIPIF1<0.（1）若SKIPIF1<0在SKIPIF1<0上存在單調(diào)遞增區(qū)間，求SKIPIF1<0的取值范圍；題型四：已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上不單調(diào)求參數(shù)1．（2021上·河南·高三校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上不是單調(diào)函數(shù)，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023上·山東濟南·高三山東省濟南市萊蕪第一中學(xué)?？茧A段練習(xí)）已知函數(shù)SKIPIF1<0在SKIPIF1<0上不是單調(diào)函數(shù)，則實數(shù)m的取值范圍是．3．（2023·全國·高三專題練習(xí)）若對于任意SKIPIF1<0，函數(shù)SKIPIF1<0在區(qū)間(t,3)上總不為單調(diào)函數(shù)，則實數(shù)m的取值范圍是．4．（2022·全國·高二專題練習(xí)）已知函數(shù)SKIPIF1<0．若SKIPIF1<0在SKIPIF1<0內(nèi)不單調(diào)，則實數(shù)a的取值范圍是．題型五：已知函數(shù)SKIPIF1<0在單調(diào)區(qū)間的個數(shù)1．（2023·全國·高三專題練習(xí)）若函數(shù)SKIPIF1<0恰有三個單調(diào)區(qū)間，則實數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0三、專項訓(xùn)練一、單選題1．（2023上·遼寧·高三校聯(lián)考階段練習(xí)）已知函數(shù)SKIPIF1<0，則“SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增”的一個充分不必要條件為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2023上·遼寧大連·高三大連市金州高級中學(xué)校考期中）若函數(shù)SKIPIF1<0在SKIPIF1<0具有單調(diào)性，則a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023上·北京·高三北京市第五中學(xué)校考階段練習(xí)）下列函數(shù)中，在區(qū)間SKIPIF1<0內(nèi)不單調(diào)的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2023上·四川遂寧·高三四川省蓬溪中學(xué)校?？茧A段練習(xí)）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是增函數(shù)，則實數(shù)SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2023下·重慶江北·高二重慶十八中校考期中）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)存在單調(diào)遞減區(qū)間，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2023下·廣東江門·高二校考期中）函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2023下·四川巴中·高二四川省通江中學(xué)?？计谥校┤艉瘮?shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，則實數(shù)SKIPIF1<0的取值范圍是()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多選題8．（2023下·高二單元測試）函數(shù)SKIPIF1<0的單調(diào)減區(qū)間可以為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．（2023下·江蘇南通·高二統(tǒng)考階段練習(xí)）若函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間為SKIPIF1<0，則SKIPIF1<0可能是（

）A．