新高考数学一轮复习精讲精练9.3 利用导数求极值最值（基础版）（原卷版）

9.3利用导数求极值最值（精讲）（基础版）思维导图思维导图考点呈现考点呈现例题剖析例题剖析考点一极值【例1-1】（2022·崇左模拟）函数SKIPIF1<0的极小值是．【例1-2】（2022·辽阳二模）设函数SKIPIF1<0，则下列不是函数SKIPIF1<0极大值点的是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例1-3】（2022·安康模拟）若函数SKIPIF1<0有两个极值点，则实数SKIPIF1<0的取值范围为（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1（2022高三上·襄阳期末）已知函数SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0所有极值点的和为（）A．SKIPIF1<0 B．13π C．17π D．SKIPIF1<02．（2022·昆明模拟）若SKIPIF1<0是函数SKIPIF1<0的极值点，则SKIPIF1<0的极大值为（）A．-1 B．SKIPIF1<0 C．SKIPIF1<0 D．13（2022·河西模拟）若函数SKIPIF1<0在SKIPIF1<0处取得极值，则SKIPIF1<0．考点二最值【例2】（2021·浙江）已知函数SKIPIF1<0，则SKIPIF1<0的最大值是_____，最小值是______．【一隅三反】1．（2021·全国专题练习）函数SKIPIF1<0的最大值为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02（2021·江苏）已知函数SKIPIF1<0，则SKIPIF1<0的最小值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2021·甘肃兰州市）函数SKIPIF1<0的最大值为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考点三已知极值最值求参数【例3-1】（2022·新疆三模）若函数SKIPIF1<0在SKIPIF1<0处有极值10，则SKIPIF1<0（）A．6 B．-15 C．-6或15 D．6或-15【例3-2】（2022·凉山模拟）函数SKIPIF1<0，若SKIPIF1<0在SKIPIF1<0上有最小值，则实数a的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例3-3】（2022高三上·开封开学考）已知函数SKIPIF1<0的值域为SKIPIF1<0，则实数SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1（2021高三上·江西月考）设函数f(x)=x3−3x，x≤a，−2x，x>a，若SKIPIF1<0无最大值，则实数A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022金台月考）已知函数SKIPIF1<0有两个极值点，则实数SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03（2022潍坊期中）若函数SKIPIF1<0在SKIPIF1<0上无极值，则实数SKIPIF1<0的取值范围（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2021·全国高三专题练习）若函数SKIPIF1<0在区间SKIPIF1<0上存在最小值，则SKIPIF1<0的取值范围是A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09.3利用导数求极值最值（精练）（基础版）题组一题组一极值1．（2022太原期中）若SKIPIF1<0是函数SKIPIF1<0的极值点，则函数（）A．有最小值SKIPIF1<0，无最大值B．有最大值SKIPIF1<0，无最小值C．有最小值SKIPIF1<0，最大值SKIPIF1<0D．无最大值，无最小值2．（2022湖北期中）已知函数SKIPIF1<0(SKIPIF1<0且SKIPIF1<0，SKIPIF1<0)的一个极值点为2，则SKIPIF1<0的最小值为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．73．（2021高三上·三门峡期中）“SKIPIF1<0”是“函数SKIPIF1<0在SKIPIF1<0上有极值”的（）A．充分不必要条件 B．必要不充分条件C．充要条件 D．既不充分也不必要条件4．（2022·镇江）已知等差数列SKIPIF1<0的前SKIPIF1<0项和为SKIPIF1<0，公差SKIPIF1<0，SKIPIF1<0和SKIPIF1<0是函数SKIPIF1<0的极值点，则SKIPIF1<0（）A．－38 B．38 C．－17 D．17题组二最值题组二最值1．（2022·淮北模拟）函数SKIPIF1<0的最大值为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．32．（2022高三上·安徽开学考）函数SKIPIF1<0的值域是．3．（2021·全国高考真题）函数SKIPIF1<0的最小值为______.4．（2021·江西高三二模）已知函数SKIPIF1<0，则SKIPIF1<0在SKIPIF1<0上的最大值是__________．5（2021·湖南）函数SKIPIF1<0的最小值为_________.6．（2022·西藏）设函数SKIPIF1<0，直线SKIPIF1<0是曲线SKIPIF1<0的切线，则SKIPIF1<0的最大值是7．（2021·全国高三专题练习（理））已知函数SKIPIF1<0在SKIPIF1<0上单调递减，则实数SKIPIF1<0的最小值是8．（2021·天津）若函数SKIPIF1<0在区间SKIPIF1<0上存在最大值，则实数SKIPIF1<0的取值范围为.题组三题组三已知极值最值求参数1．（2022·莆田三模）已知函数SKIPIF1<0的最小值是4．则SKIPIF1<0（）A．3 B．4 C．5 D．62．（2021高三上·湖北期中）若函数SKIPIF1<0（SKIPIF1<0为常数）有两个不同的极值点，则实数SKIPIF1<0取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022湖南）已知f(x)＝SKIPIF1<0x3＋(a－1)x2＋x＋1没有极值，则实数a的取值范围是（）A．[0，1] B．(－∞，0]∪[1，＋∞)C．[0，2] D．(－∞，0]∪[2，＋∞)4．（2022辽宁月考）已知函数SKIPIF1<0在SKIPIF1<0上恰有两个极值点，则SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2022河南月考）已知函数SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）存在极大值和极小值，且极大值与极小值互为相反数，则（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2021高三上·邢台月考）若函数SKIPIF1<0在区间SKIPIF1<0有最小值，则实数SKIPI