新高考数学一轮复习讲与练第07讲 一元函数的导数及其应用（练）（原卷版）

第01讲一元函数的导数及其应用（一）1．若“SKIPIF1<0，使SKIPIF1<0成立”是假命题，则实数λ的取值范围是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．若函数SKIPIF1<0，满足SKIPIF1<0恒成立，则SKIPIF1<0的最大值为（

）A．3 B．4 C．SKIPIF1<0 D．SKIPIF1<03．下列求导运算错误的是（

）.A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．若函数SKIPIF1<0处有极大值，则常数SKIPIF1<0的值为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05、在曲线SKIPIF1<0的所有切线中，与直线SKIPIF1<0平行的共有（

）．A．1条 B．2条 C．3条 D．4条6．已知SKIPIF1<0是函数SKIPIF1<0的导数，且SKIPIF1<0，当SKIPIF1<0时，SKIPIF1<0，则不等式SKIPIF1<0的解集是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．若函数SKIPIF1<0在区间SKIPIF1<0内单调递增，则实数SKIPIF1<0的取值范围为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知函数SKIPIF1<0，SKIPIF1<0，记SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，则SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，的大小关系为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．若SKIPIF1<0且SKIPIF1<0，SKIPIF1<0且SKIPIF1<0，SKIPIF1<0且SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<010．若函数SKIPIF1<0恰有2个不同的零点，则实数m的值是_________.11．已知函数SKIPIF1<0．(1)讨论函数SKIPIF1<0在区间SKIPIF1<0上的单调性；(2)当SKIPIF1<0时，证明：SKIPIF1<0．1．已知SKIPIF1<0，且满足SKIPIF1<0，则下列正确的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0（多选）2．已知函数SKIPIF1<0，若SKIPIF1<0，则SKIPIF1<0可取（

）A．1 B．2 C．SKIPIF1<0 D．SKIPIF1<0（多选）3．已知SKIPIF1<0，函数SKIPIF1<0的导函数为SKIPIF1<0，下列说法正确的是（

）A．SKIPIF1<0 B．单调递增区间为SKIPIF1<0C．SKIPIF1<0的极大值为SKIPIF1<0 D．方程SKIPIF1<0有两个不同的解4．已知正三棱锥的各顶点都在同一球面上，若该球的表面积为SKIPIF1<0，则该正三棱锥体积的最大值为___________.5．设SKIPIF1<0，则SKIPIF1<0的大小关系是___________.6．已知函数SKIPIF1<0，若关于SKIPIF1<0的不等式SKIPIF1<0的解集为SKIPIF1<0，则实数SKIPIF1<0的取值范围是___________.7．过点SKIPIF1<0作曲线SKIPIF1<0的切线，若切线有且只有两条，则实数SKIPIF1<0的取值范围是___________.8．若函数SKIPIF1<0，则曲线SKIPIF1<0在点SKIPIF1<0处的切线方程为___________.9．已知函数SKIPIF1<0(1)当SKIPIF1<0时，求函数SKIPIF1<0的单调区间；(2)若函数SKIPIF1<0有3个不同零点，求实数SKIPIF1<0的取值范围.10．已知函数SKIPIF1<0．(1)若SKIPIF1<0，求曲线SKIPIF1<0在点SKIPIF1<0处的切线方程；(2)若SKIPIF1<0，试讨论函数SKIPIF1<0的零点个数．11．若SKIPIF1<0是函数SKIPIF1<0的极值点，则SKIPIF1<0______；SKIPIF1<0的极大值为______.1．（2022·全国·高考真题（理））当SKIPIF1<0时，函数SKIPIF1<0取得最大值SKIPIF1<0，则SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．12．（2022·全国·高考真题（文））函数SKIPIF1<0在区间SKIPIF1<0的最小值、最大值分别为（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·全国·高考真题（理））已知SKIPIF1<0，则（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2010·全国·高考真题（文））若曲线y＝x2＋ax＋b在点(0，b)处的切线方程是x－y＋1＝0，则（

）A．a＝1，b＝1 B．a＝－1，b＝1C．a＝1，b＝－1 D．a＝－1，b＝－15．（2015·安徽·高考真题（文））函数f（x）＝ax3+bx2+cx+d的图象如图所示，则下列结论成立的是（

）A．a＞0，b＜0，c＞0，d＞0 B．a＞0，b＜0，c＜0，d＞0C．a＜0，b＜0，c＜0，d＞0 D．a＞0，b＞0，c＞0，d＜06．（2009·宁夏·高考真题（文））曲线SKIPIF1<0在点(0，1)处的切线方程为________．7．（2022·全国·高考真题（文））已知函数SKIPIF1<0．(1)当SKIPIF1<0时，求SKIPIF1<0的最大值；(2)若SKIPIF1<0恰有一个零点，求a的取值范围．8．（2022·全国·高考真题（文））已知函数SKIPIF1<0，曲线SKIPIF1<0在点SKIPIF1<0处的切线也是曲线SKIPIF1<0的切线．(1)若SKIPIF1<0，求a；(2)求a的取值范围．9．（2022·全国·高考真题（理））已知函数SKIPIF1<0