新高考数学二轮复习 题型归纳演练专题3-2 利用导数解决单调性中求参数问题（选填）（原卷版）

专题3-2利用导数解决单调性中求参数问题（选填）TOC\o"1-1"\h\u 1题型一：已知函数SKIPIF1<0在区间SKIPIF1<0上单调 1题型二：已知函数SKIPIF1<0在区间SKIPIF1<0上存在单调区间 3题型三：已知函数SKIPIF1<0在区间SKIPIF1<0上不单调 4题型四：已知函数SKIPIF1<0的单调区间恰为SKIPIF1<0 5题型五：已知函数SKIPIF1<0有三个单调区间 6 7题型一：已知函数SKIPIF1<0在区间SKIPIF1<0上单调【典型例题】例题1．（2022·重庆市第七中学校高二阶段练习）若函数SKIPIF1<0在区间SKIPIF1<0单调递增，则SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例题2．（2022·全国·高二课时练习）若函数SKIPIF1<0在区间SKIPIF1<0内单调递减，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例题3．（2022·陕西咸阳中学高三阶段练习（理））已知函数SKIPIF1<0，若对SKIPIF1<0，SKIPIF1<0，都有SKIPIF1<0成立，则SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【提分秘籍】已知函数SKIPIF1<0在区间SKIPIF1<0上单调①已知SKIPIF1<0在区间SKIPIF1<0上单调递增SKIPIF1<0SKIPIF1<0，SKIPIF1<0恒成立.②已知SKIPIF1<0在区间SKIPIF1<0上单调递减SKIPIF1<0SKIPIF1<0，SKIPIF1<0恒成立.注：已知单调性，等价条件中的不等式含等号.【变式演练】1．（2021·四川·宜宾市叙州区第一中学校高二阶段练习（文））若SKIPIF1<0在SKIPIF1<0上是减函数，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全国·高三专题练习）设函数SKIPIF1<0在SKIPIF1<0上单调递减，则实数a的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·陕西省宝鸡市长岭中学高二期中（理））若函数SKIPIF1<0在SKIPIF1<0上是增函数，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·山西临汾·高三期中）设函数SKIPIF1<0，若对任意SKIPIF1<0，SKIPIF1<0恒成立，则SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0题型二：已知函数SKIPIF1<0在区间SKIPIF1<0上存在单调区间【典型例题】例题1．（2022·江西·上高二中高二阶段练习（文））若函数SKIPIF1<0存在单调递减区间，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0例题2．（2022·全国·高三专题练习）若函数SKIPIF1<0存在单调递增区间，则SKIPIF1<0的取值范围是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【提分秘籍】已知函数SKIPIF1<0在区间SKIPIF1<0上存在单调区间①已知SKIPIF1<0在区间SKIPIF1<0上存在单调增区间SKIPIF1<0SKIPIF1<0，SKIPIF1<0有解.②已知SKIPIF1<0在区间SKIPIF1<0上存在单调减区间SKIPIF1<0SKIPIF1<0，SKIPIF1<0有解.【变式演练】1．（2022·全国·高三专题练习）若函数SKIPIF1<0在SKIPIF1<0存在单调递减区间，则实数SKIPIF1<0的取值范围是A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·福建·福州黎明中学高三阶段练习）若函数f(x)＝x2－4ex－ax在R上存在单调递增区间，则实数a的取值范围为__________．题型三：已知函数SKIPIF1<0在区间SKIPIF1<0上不单调【典型例题】例题1．（2022·陕西·蒲城县蒲城中学高三阶段练习（文））已知函数SKIPIF1<0在SKIPIF1<0上不单调，则SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例题2．（2022·广西河池·高二阶段练习（理））若函数SKIPIF1<0在定义域内的一个子区间SKIPIF1<0上不是单调函数，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【提分秘籍】已知函数SKIPIF1<0在区间SKIPIF1<0上不单调SKIPIF1<0SKIPIF1<0，使得SKIPIF1<0（其中SKIPIF1<0为变号零点）【变式演练】1．（2022·安徽·合肥一中高二阶段练习）若函数SKIPIF1<0在其定义域上不单调，则实数SKIPIF1<0的取值范围为（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·四川省资阳中学高二期中（理））已知函数SKIPIF1<0在区间SKIPIF1<0上不单调，则实数SKIPIF1<0的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·江西·金溪一中高二阶段练习（理））已知函数SKIPIF1<0在SKIPIF1<0内不是单调函数，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·上海大学市北附属中学高一期中）若函数SKIPIF1<0在区间SKIPIF1<0上不是单调函数，则实数SKIPIF1<0的取值范围________.题型四：已知函数SKIPIF1<0的单调区间恰为SKIPIF1<0【典型例题】例题1．（2021·四川省成都市玉林中学高二期中（文））已知函数SKIPIF1<0在SKIPIF1<0单调递增，在SKIPIF1<0单调递减，则函数SKIPIF1<0在SKIPIF1<0的值域是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0例题2．（2022·全国·高二课时练习）已知函数SKIPIF1<0在SKIPIF1<0、SKIPIF1<0上为增函数，在SKIPIF1<0上为减函数，则实数SKIPIF1<0的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【变式演练】1．（2022·全国·高二课时练习）已知函数SKIPIF1<0的单调递增区间是SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·福建漳州·高二期末）已知函数SKIPIF1<0的单调递减区间是SKIPIF1<0，则关于SKIPIF1<0的不等式SKIPIF1<0的解集是__________.题型五：已知函数SKIPIF1<0有三个单调区间【典型例题】例题1．（2019·河北省隆化存瑞中学高三阶段练习（理））若函数SKIPIF1<0恰好有三个单调区间，则实数SKIPIF1<0的取值范围为A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<0例题2．（2019·江苏盐城·一模）已知函数SKIPIF1<0，若函数SKIPIF1<0存在三个单调区间，则实数SKIPIF1<0的取值范围是__________.【提分秘籍】已知函数SKIPIF1<0有三个单调区间SKIPIF1<0SKIPIF1<0有两个不同的实数根.【变式演练】1．（2022·宁夏·永宁县文昌中学高三期末（文））若函数SKIPIF1<0有三个单调区间，则SKIPIF1<0的取值范围是________________．2．（2022·江西省信丰中学高二阶段练习（文））若函数SKIPIF1<0在定义域SKIPIF1<0上恰有三个单调区间，则SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2016·黑龙江双鸭山·高二阶段练习）若函数恰有三个单调区间，则实数的取值范围为A． B．C． D．4．（2020·全国·高三专题练习）已知函数SKIPIF1<0恰有三个单调区间，则实数SKIPIF1<0的取值范围是__________．一、单选题1．（2019·四川自贡·高二期末（理））函数SKIPIF1<0恰有SKIPIF1<0个单调区间的必要不充分条件是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2019·河北省隆化存瑞中学高三阶段练习（理））若函数SKIPIF1<0恰好有三个单调区间，则实数SKIPIF1<0的取值范围为A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<03．（2022·河南·驻马店市第二高级中学高三阶段练习（文））若函数SKIPIF1<0在区间SKIPIF1<0上单调递增，则SKIPIF1<0的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2021·江苏·张家港高级中学高三期中）若函数SKIPIF1<0在区间SKIPIF1<0内存在单调递增区间，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2023·全国·高三专题练习）若函数SKIPIF1<0在其定义域的一个子区间SKIPIF1<0内不是单调函数，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022·福建福州·高三期中）已知函数SKIPIF1<0，对任意的实数SKIPIF1<0，且SKIPIF1<0，不等式SKIPIF1<0恒成立，则实数a的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2023·全国·高三专题练习）已知函数SKIPIF1<0在区间SKIPIF1<0上不是单调函数，则实数SKIPIF1<0的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0