新高考数学一轮复习百题刷过关专题32 导数几何意义问题必刷100题(原卷版)

专题32导数几何意义问题必刷100题类型一:求在曲线上一点的切线方程1-10题1．已知SKIPIF1<0，则在曲线SKIPIF1<0上一点SKIPIF1<0处的切线方程为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．设函数SKIPIF1<0.若SKIPIF1<0为奇函数，则曲线SKIPIF1<0在点SKIPIF1<0处的切线方程为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．曲线SKIPIF1<0在点SKIPIF1<0处的切线方程是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．已知函数SKIPIF1<0是奇函数且其图象在点SKIPIF1<0处的切线方程SKIPIF1<0，设函数SKIPIF1<0，则SKIPIF1<0的图象在点SKIPIF1<0处的切线方程为（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．曲线SKIPIF1<0在SKIPIF1<0处的切线的倾斜角为SKIPIF1<0，则SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知函数SKIPIF1<0为奇函数，则SKIPIF1<0在SKIPIF1<0处的切线方程为（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．已知函数SKIPIF1<0在R上满足SKIPIF1<0，则曲SKIPIF1<0在点SKIPIF1<0处的切线方程是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．曲线SKIPIF1<0在点SKIPIF1<0处的切线与两坐标轴围成的三角形的面积为（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．若函数SKIPIF1<0图象在点SKIPIF1<0处的切线方程为SKIPIF1<0，则SKIPIF1<0的最小值为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．已知SKIPIF1<0是曲线SKIPIF1<0上的任一点，若曲线在SKIPIF1<0点处的切线的倾斜角均是不小于SKIPIF1<0的锐角，则实数SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0类型二:求过一点的切线方程1-10题1．函数SKIPIF1<0过点SKIPIF1<0的切线方程为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知函数SKIPIF1<0，若直线SKIPIF1<0过点SKIPIF1<0，且与曲线SKIPIF1<0相切，则直线SKIPIF1<0的斜率为（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．己知函数SKIPIF1<0，函数SKIPIF1<0，若两函数的图象恰有两个不同的交点，则实数k的取值范围（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知曲线SKIPIF1<0的切线过坐标原点，则此切线的斜率为（）A．e B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．若过点SKIPIF1<0可以作曲线SKIPIF1<0的两条切线，则（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．若直线l与曲线y=SKIPIF1<0和x2+y2=SKIPIF1<0都相切，则l的方程为（）A．y=2x+1 B．y=2x+SKIPIF1<0 C．y=SKIPIF1<0x+1 D．y=SKIPIF1<0x+SKIPIF1<07．已知SKIPIF1<0.若曲线SKIPIF1<0存在两条过SKIPIF1<0点的切线，则SKIPIF1<0的取值范围是___________.8．已知函数SKIPIF1<0，过点作SKIPIF1<0曲线SKIPIF1<0的切线，则函数的切线方程为_______________________．9．已知双曲线SKIPIF1<0的一条渐近线与曲线SKIPIF1<0相切，则该双曲线的离心率为______.10．设函数SKIPIF1<0，若SKIPIF1<0为奇函数，则过点SKIPIF1<0且与曲线SKIPIF1<0相切的直线方程为________.类型三:距离问题1-10题1．已知抛物线SKIPIF1<0焦点为SKIPIF1<0是抛物线SKIPIF1<0上一点，且SKIPIF1<0，点SKIPIF1<0在抛物线SKIPIF1<0上运动，则点SKIPIF1<0到直线SKIPIF1<0的最小距离是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．点P在函数SKIPIF1<0的图像上，若满足到直线SKIPIF1<0的距离为SKIPIF1<0的点P有且仅有3个，则实数a的值为（）A．5或SKIPIF1<0 B．1或3 C．1 D．53．若点SKIPIF1<0在曲线SKIPIF1<0上运动，点SKIPIF1<0在直线SKIPIF1<0上运动，SKIPIF1<0两点距离的最小值为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．若点SKIPIF1<0与曲线SKIPIF1<0上点SKIPIF1<0距离最小值为SKIPIF1<0，则实数SKIPIF1<0为A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．曲线SKIPIF1<0在点（1,1）处的切线为SKIPIF1<0，则SKIPIF1<0上的点到圆SKIPIF1<0上的点的最近距离是A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．在平面直角坐标系SKIPIF1<0中，SKIPIF1<0是曲线SKIPIF1<0SKIPIF1<0上的一个动点，则点SKIPIF1<0到直线SKIPIF1<0的距离的最小值是____________.7．设P为ySKIPIF1<0x2﹣2图象C上任意一点，l为C在点P处的切线，则坐标原点O到l距离的最小值为_____.8．设SKIPIF1<0为SKIPIF1<0图象SKIPIF1<0上任意一点，SKIPIF1<0为SKIPIF1<0在点SKIPIF1<0处的切线，则坐标原点SKIPIF1<0到SKIPIF1<0距离的最小值为_______.9．曲线SKIPIF1<0在点(1,1)处的切线为l，则l上的点到圆SKIPIF1<0上的点的最近距离是________．10．定义：曲线C上的点到直线l的距离的最小值称为曲线C到直线l的距离．已知曲线C1：y＝x2＋a到直线l：y＝x的距离等于C2：x2＋(y＋4)2＝2到直线l：y＝x的距离，则实数a＝______________．类型四:零点问题1-10题1．已知函数SKIPIF1<0，若函数SKIPIF1<0有四个零点，则实数SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．设SKIPIF1<0，若函数SKIPIF1<0在区间SKIPIF1<0上有三个零点，则实数SKIPIF1<0的取值范围是A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知SKIPIF1<0，若存在实数SKIPIF1<0，使得SKIPIF1<0在SKIPIF1<0上有2个零点，则SKIPIF1<0的取值范围为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知函数SKIPIF1<0且关于SKIPIF1<0的方程SKIPIF1<0有三个不等实根，则实数SKIPIF1<0的取值范围为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知函数SKIPIF1<0，若SKIPIF1<0存在3个零点，则a的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知函数SKIPIF1<0满足SKIPIF1<0，且SKIPIF1<0时，SKIPIF1<0，若SKIPIF1<0时，方程SKIPIF1<0有三个不同的根，则SKIPIF1<0的取值范围为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知函数SKIPIF1<0有两个不同的零点，则实数a的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．定义在SKIPIF1<0上的函数SKIPIF1<0满足SKIPIF1<0，且SKIPIF1<0时，SKIPIF1<0.若关于SKIPIF1<0的方程SKIPIF1<0有三个不相等的实数根，则实数SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<09．已知函数SKIPIF1<0，SKIPIF1<0，若函数SKIPIF1<0有两个零点，则SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．已知函数SKIPIF1<0，若函数SKIPIF1<0恰有一个零点，则SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0类型五:求参数问题1-10题1．已知函数SKIPIF1<0，若不等式SKIPIF1<0对任意的SKIPIF1<0恒成立，则实数SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．若曲线SKIPIF1<0与SKIPIF1<0有一条斜率为2的公切线，则SKIPIF1<0=（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知SKIPIF1<0的最小值为0，则正实数SKIPIF1<0的最小值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．14．已知函数SKIPIF1<0的图象在SKIPIF1<0处的切线方程为SKIPIF1<0，若SKIPIF1<0恒成立，则SKIPIF1<0的取值范围为（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．若曲线SKIPIF1<0与曲线SKIPIF1<0存在公切线，则实数SKIPIF1<0的取值范围（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．若曲线SKIPIF1<0上存在两条垂直于SKIPIF1<0轴的切线，则SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．若函数SKIPIF1<0图象上任意一点的切线斜率均大于SKIPIF1<0，则实数SKIPIF1<0的取值范围是________.8．设函数SKIPIF1<0的图象在点SKIPIF1<0处的切线为SKIPIF1<0，若方程SKIPIF1<0有两个不等实根，则实数SKIPIF1<0的取值范围是__________．9．已知k为常数，函数SKIPIF1<0，若关于x的函数SKIPIF1<0有4个零点，则实数k的取值范围为________.10．若直线SKIPIF1<0是曲线SKIPIF1<0的切线，也是曲线SKIPIF1<0的切线，则SKIPIF1<0________.类型六:导数几何意义综合压轴小题1-50题一、单选题1．过SKIPIF1<0引抛物线SKIPIF1<0的切线，切点分别为A，SKIPIF1<0.若SKIPIF1<0的斜率等于2，则SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．22．关于函数SKIPIF1<0，下列判断错误的是（）A．函数SKIPIF1<0的图象在SKIPIF1<0处的切线方程为SKIPIF1<0B．SKIPIF1<0是函数SKIPIF1<0的一个极值点C．当SKIPIF1<0时，SKIPIF1<0D．当SKIPIF1<0时，不等式SKIPIF1<0的解集为SKIPIF1<03．函数SKIPIF1<0与SKIPIF1<0的图象上存在关于SKIPIF1<0轴的对称点，则实数SKIPIF1<0的取值范围为（）(SKIPIF1<0为自然对数的底)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．若过点SKIPIF1<0可以作曲线SKIPIF1<0的两条切线，则（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．已知直线SKIPIF1<0与函数SKIPIF1<0的图象有且仅有两个公共点，若这两个公共点的横坐标分别为SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，则下列说法正确的是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．一条倾斜角为SKIPIF1<0的直线与执物线SKIPIF1<0交于不同的SKIPIF1<0两点，设弦SKIPIF1<0的中点为SKIPIF1<0过SKIPIF1<0作平行于SKIPIF1<0轴的直线交抛物线于点SKIPIF1<0，则以SKIPIF1<0为切点的抛物线的切线的斜率为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知函数SKIPIF1<0，若曲线SKIPIF1<0在点SKIPIF1<0处的切线经过原点，则SKIPIF1<0的值为（）A．-2 B．3C．-1 D．-38．已知偶函数SKIPIF1<0满足SKIPIF1<0，且在SKIPIF1<0处的导数SKIPIF1<0，则曲线SKIPIF1<0在SKIPIF1<0处的切线方程为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．已知曲线SKIPIF1<0在点SKIPIF1<0处的切线与直线SKIPIF1<0垂直，若SKIPIF1<0，SKIPIF1<0是函数SKIPIF1<0的两个零点，则（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．已知函数SKIPIF1<0有两个零点，则实数m的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．已知函数SKIPIF1<0与SKIPIF1<0的图象上存在关于直线SKIPIF1<0对称的点，若点SKIPIF1<0，SKIPIF1<0分别在SKIPIF1<0，SKIPIF1<0的图象上，则当SKIPIF1<0取最大值时，SKIPIF1<0的最小值是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．已知SKIPIF1<0，若函数SKIPIF1<0有4个零点，则实数SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．若函数SKIPIF1<0（SKIPIF1<0为常数）存在两条均过原点的切线，则实数SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<014．已知函数SKIPIF1<0，若过点SKIPIF1<0可作曲线SKIPIF1<0的三条切线，则SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．已知函数SKIPIF1<0，方程SKIPIF1<0恰有两个根，记较大的根为SKIPIF1<0，则SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<016．已知函数SKIPIF1<0，若方程SKIPIF1<0有且仅有两个不同的解，则实数m的值为（）A．2e B．4e C．6e D．8e17．若关于SKIPIF1<0的方程SKIPIF1<0恰有三个不同的解，则实数SKIPIF1<0的取值范围为（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<018．将函数SKIPIF1<0的图象向左平移SKIPIF1<0个单位后得到函数SKIPIF1<0的图象，SKIPIF1<0的图象在SKIPIF1<0处切线垂直于y轴，且SKIPIF1<0，则当SKIPIF1<0取最小正数时，不等式SKIPIF1<0的解集是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<019．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（）A．SKIPIF1<0 B．1 C．SKIPIF1<0 D．SKIPIF1<020．已知函数SKIPIF1<0，若SKIPIF1<0，则a的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<021．过直线SKIPIF1<0上一点SKIPIF1<0可以作曲线SKIPIF1<0两条切线，则点SKIPIF1<0横坐标SKIPIF1<0的取值范围为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<022．已知a为常数，函数SKIPIF1<0有两个极值点x1，x2(x1＜x2)，则下列结论正确的是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<023．若存在SKIPIF1<0，使得函数SKIPIF1<0与SKIPIF1<0的图象在这两个函数图象的公共点处的切线相同，则SKIPIF1<0的最大值为SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<024．已知函数SKIPIF1<0，方程SKIPIF1<0有4个不同的实数根，则SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<025．已知函数SKIPIF1<0，若方程SKIPIF1<0有4个零点，则SKIPIF1<0的可能的值为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<026．已知函数SKIPIF1<0，函数SKIPIF1<0，若方程SKIPIF1<0恰有三个实数解，则实数SKIPIF1<0的取值范围为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<027．已知函数SKIPIF1<0，若函数SKIPIF1<0恰有三个零点，则实数SKIPIF1<0的取值范围是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<028．已知直线SKIPIF1<0与曲线SKIPIF1<0有且只有两个公共点SKIPIF1<0，其中SKIPIF1<0，则SKIPIF1<0（）A．SKIPIF1<0 B．0 C．1 D．SKIPIF1<029．已知函数SKIPIF1<0，则函数SKIPIF1<0的零点个数为（）A．6 B．5 C．4 D．330．已知函数SKIPIF1<0在SKIPIF1<0上的最小值为3，直线l在y轴上的截距为SKIPIF1<0，则下列结论正确是（）①实数SKIPIF1<0；②直线l的斜率为1时，SKIPIF1<0是曲线SKIPIF1<0的切线；③曲线SKIPIF1<0与直线l有且仅有一个交点.A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、多选题31．已知函数SKIPIF1<0（SKIPIF1<0为自然对数的底数），过点SKIPIF1<0作曲线SKIPIF1<0的切线.下列说法正确的是（）A．当SKIPIF1<0时，若只能作两条切线，则SKIPIF1<0B．当SKIPIF1<0，SKIPIF1<0时，则可作三条切线C．当SKIPIF1<0时，可作三条切线，则SKIPIF1<0D．当SKIPIF1<0，SKIPIF1<0时，有且只有一条切线32．已知函数SKIPIF1<0，SKIPIF1<0，若x1、x2、x3，x4是方程SKIPIF1<0仅有的4个解，且x1<x2<x3<x4，则（）A．0<x1x2<1 B．x1x2>1C．SKIPIF1<0 D．SKIPIF1<033．关于函数SKIPIF1<0，SKIPIF1<0.下列说法正确的是（）A．SKIPIF1<0在SKIPIF1<0处的切线方程为SKIPIF1<0B．SKIPIF1<0有两个零点C．SKIPIF1<0有两个极值点D．SKIPIF1<0存在唯一极小值点SKIPIF1<0，且SKIPIF1<034．已知函数SKIPIF1<0，则下列结论中正确的是（）A．若SKIPIF1<0在区间SKIPIF1<0上的最大值与最小值分别为SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0B．曲线SKIPIF1<0与直线SKIPIF1<0相切C．若SKIPIF1<0为增函数，则SKIPIF1<0的取值范围为SKIPIF1<0D．SKIPIF1<0在SKIPIF1<0上最多有SKIPIF1<0个零点35．某数学研究小组在研究牛顿三叉戟曲线SKIPIF1<0时通过数学软件绘制出其图象（如图），并给出以下几个结论，则正确的有（）A．函数SKIPIF1<0的极值点有且只有一个B．当SKIPIF1<0时，SKIPIF1<0恒成立C．过原点且与曲线SKIPIF1<0相切的直线有且仅有2条D．若SKIPIF1<0，则SKIPIF1<0的最小值为SKIPIF1<036．已知函数SKIPIF1<0，则下列说法正确的是（）A．若SKIPIF1<0，则曲线SKIPIF1<0在SKIPIF1<0处的切线与SKIPIF1<0相互平行B．函数SKIPIF1<0在[1，4]上单调递増的必要不充分条件是SKIPIF1<0C．记函数SKIPIF1<0的最小值为SKIPIF1<0，则SKIPIF1<0D．若SKIPIF1<0，SKIPIF1<0，使得SKIPIF1<0在SKIPIF1<0恒成立，则SKIPIF1<0的最大值为337．函数SKIPIF1<0的图象（如图）称为牛顿三叉戟曲线，则（）A．SKIPIF1<0的极小值点为SKIPIF1<0B．当SKIPIF1<0时，SKIPIF1<0C．过原点且与曲线SKIPIF1<0相切的直线仅有2条D．若SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0的最小值为SKIPIF1<038．设函数SKIPIF1<0，若曲线SKIPIF1<0在点SKIPIF1<0处的切线与该曲线恰有一个公共点SKIPIF1<0，则选项中满足条件的SKIPIF1<0有（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<039．已知函数SKIPIF1<0，则（）A．若SKIPIF1<0，则函数SKIPIF1<0有2个极值点B．若关于SKIPIF1<0的不等式函数SKIPIF1<0在SKIPIF1<0上恒成立，则实数SKIPIF1<0的取值范围为SKIPIF1<0C．若曲线SKIPIF1<0在SKIPIF1<0处的切线与SKIPIF1<0相互垂直，则SKIPIF1<0D．若SKIPIF1<0，则函数SKIPIF1<0