2024最新整理、试题、试卷精品资料 2024届高考数学二轮复习专题二函数与导数专题能力训练7
导数与函数的单调性极值最值理
能力突破训练
1.已知函数f(x)的导函数为f'(x),且满足f(x)=af'(1)x+ln x,若
f'=0,则a=()
D.2
C.1
B.-2
A.-1
2.(2017浙江,7)函数y=f(x)的导函数y=f'(x)的图象如图所示,则函
数y=f(x)的图象可能是()
3.若定义在R上的函数f(x)满足f(0)=-1,其导函数f'(x)满足f'(x)>k>1,则下列结论中一定错误的是
A.f
B.f
C.f
D.f
4.已知常数a,b,c都是实数,f(x)=ax3+bx2+cx-34的导函数为f'(x),f'(x)≤0的解集为{x|-2≤x≤3}.若f(x)的极小值等于-115,
则a的值是()
But how to read happily is a difficult part for us, I think we need to take several steps to get happiness. The first step, you should choose a good book, which you really want to read. The second step,- 1 - / 15
()
2024最新整理、试题、试卷精品资料
B.
A.-C.2
D.5
5.若直线y=kx+b是曲线y=ln x+2的切线,也是曲线y=ln(x+1)的切线,
则b=.
6.在曲线y=x3+3x2+6x-1的切线中,斜率最小的切线方程为.
7.设函数f(x)=aex++b(a>0).(1)求f(x)在[0,+∞)上的最小值;
(2)设曲线y=f(x)在点(2,f(2))处的切线方程为y=x,求a,b的值.
8.设函数f(x)=xea-x+bx,曲线y=f(x)在点(2,f(2))处的切线方程为
y=(e-1)x+4.
(1)求a,b的值;
(2)求f(x)的单调区间.
9.设a>1,函数f(x)=(1+x2)ex-a.
(1)求f(x)的单调区间;
(2)证明:f(x)在区间(-∞,+∞)上仅有一个零点;
(3)若曲线y=f(x)在点P处的切线与x轴平行,且在点M(m,n)处的切线
与直线OP平行(O是坐标原点),证明:m≤-1.
10.已知函数f(x)=x3+x2-ax-a,x∈R,其中a>0.
(1)求函数f(x)的单调区间;
(2)若函数f(x)在区间(-2,0)内恰有两个零点,求a的取值范围;
But how to read happily is a difficult part for us, I think we need to take several steps to get happiness. The first step, you should choose a good book, which you really want to read. The second step,- 2 - / 15
2024最新整理、试题、试卷精品资料 (3)当a=1时,设函数f(x)在区间[t,t+3]上的最大值为M(t),最小值为
m(t),记g(t)=M(t)-m(t),求函数g(t)在区间[-3,-1]上的最小值.
思维提升训练
11.(2017陕西咸阳二模)已知定义在R上的函数f(x)的导函数为
f'(x),对任意x∈R满足f(x)+f'(x)<0,则下列结论正确的是()
B.e2f(2) A.e2f(2)>e3f(3)C.e2f(2)≥e3f(3) 12.已知f'(x)为定义在R上的函数f(x)的导函数,对任意实数x,都有f(x) 13.已知函数f(x)=. (1)求函数f(x)的单调区间; (2)当x>0时,若f(x)>恒成立,求整数k的最大值. 14.已知函数f(x)=ln x-ax2+x,a∈R. (1)若f(1)=0,求函数f(x)的单调递减区间; (2)若关于x的不等式f(x)≤ax-1恒成立,求整数a的最小值;a=-2,正实数 x1,x2 满足 f(x1)+f(x2)+x1x2=0,求 证:x1+x2≥. (3)若 15.(2017山东,理20)已知函数f(x)=x2+2cos x,g(x)=ex(cos x-sin x+2x-2),其中e≈2.718 28…是自然对数的底数.(1)求曲线y=f(x)在点(π,f(π))处的切线方程. But how to read happily is a difficult part for us, I think we need to take several steps to get happiness. The first step, you should choose a good book, which you really want to read. The second step,- 3 - / 15
2024届高考数学二轮复习专题二函数与导数专题能力训练7导数与函数的单调性极值最值理
