组卷网>知识点选题>利用导数证明或求解函数单调区间(不含参)
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2 . 在①曲线yfx)在点eqId1d6c5af8db6b41ecb2e767ab9088ebb1处的切线与y轴垂直,②fx)的导数eqId67275592f85f400ab271f455b71d45c3的最小值为﹣eqId44aff622a095465082b61837e24439e7,③函数fx)在区间eqIddefaf010132c4ca5a1dd2ed9dddbc7f3上是减函数,在区间eqIdcef986329fec4bc69b27f2e3b1ee753f上是增函数.这三个条件中任选一个补充在横线上,并回答下面问题.
已知函数fx)=x3+ax+b,且满足 ____.
(1)求a值;
(2)若函数yfx)在区间[﹣1,2]上的最大值与最小值的和为7,求b值.
4 . 已知函数eqId847d4b54cf9f4fca86d2e64fd11bf833eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7为常数),且eqIdc5faa3a08c944a41850c52572707bcadeqId6f13759e937144069819aed2ae5a1057 的一个极值点.
(1)求eqId70a27b6ddf6b478285353abb3b1f3741的值;
(2)求函数eqId6f13759e937144069819aed2ae5a1057的单调区间;
(3)若函数eqId144eff5c0e4649138a21f2b1b6a06907有3个不同的零点,求实数eqIdaea992e70d4943e49e893817eb885ed7的取值范围.
5 . 已知f(x)是定义在R上的奇函数,且当x>0时,eqIdeb32f99dd98b491c806c8f0438dc7ad3,则(   )
A.f(4)>ef(3)B.f(﹣4)>e2f(﹣2)
C.e2f(4)<f(2)D.ef(﹣4)>f(﹣3)
6 . 下列函数在定义域内是增函数的有(   )
A.eqIde7960ae7b12d46f39a549af1b3872f97B.eqId059a304fe3e445de978203c5a33f4df5
C.eqId61c16cf2da2d495cb687f636ffced712D.eqId9179353c143746d8982cae0206f06307
7 . 已知函数eqId05b44ede28194c2884a687ecfc0842e1,则下列结论中正确的是(   )
A.函数eqId10852d81bc184140a7780250c82c6929eqId28ace4570ea84d189b85258609ba6e4a上单调递减
B.函数eqId10852d81bc184140a7780250c82c6929的极小值点为eqIdc8c5b1538b4d4d2a9e0ba1ab96db958c
C.函数eqId10852d81bc184140a7780250c82c6929无极大值
D.函数eqId10852d81bc184140a7780250c82c6929eqIda75f32d729e345fca573383b8c130842上的最大值为eqId1d18010fc29e4f45abaaece953793246
8 . 已知函数eqId686c8b6b1c284d6781ce70e789d332df.
(1)当eqIda08ce385279d41c789695fb651b17890时,求函数eqId10852d81bc184140a7780250c82c6929的单调区间;
(2)若存在eqId2a62f605191f45dbb5c956692568011e,使不等式eqIdaed2724d9cdf4efab919648e91d39188成立,求实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围.
9 . 对于函数eqId9c41c45d1ba54850b8eb3de782cd9556,下列说法正确的是(   )
A.eqId6f13759e937144069819aed2ae5a1057eqIdb2a911b84483486cb5698cc9ba35cac7上单调递增,在eqIded88fd52ab66441d9139a1279ba56fb7上单调递减
B.若方程eqIda30fdd0ecd7342698f169d48d79c16a6eqIdddd35c5d043e4ebeac32a99367053c68个不等的实根,则eqId409e429212964b028ba31840a4cffca0
C.当eqId6dd8338790114626a97c389b18e2cc95时,eqId3398609b28bb499ea6b675058c78f78a
D.设eqId4fc37e5283e4473e8d1863bea74325e3,若对eqId4503c7d796a8478cb65d03c9477200f0eqIdfa8ec6f5355b4c65829f865ffde0e6c7,使得eqId65e395e41edd48daa108ab4a9db9b3d3成立,则eqIdb5db9563dd1a4e139f5425eda442560e
10 . 已知函数eqId10852d81bc184140a7780250c82c6929的定义域是eqIddca4c31f92e1447fb6eceb9fdf294175,且满足eqIdd10480291c1e4067a867195c233e2eefeqId2a572f01ebe94a1686fe4c0c8f50d3fb(其中eqIdf035b8f27d4645bb9f6a66f4a3f51918为自然常数,eqId592860922d9541209c48c5ffb5be52fb),则下列说法正确的是(   )
A.eqId10852d81bc184140a7780250c82c6929eqIddca4c31f92e1447fb6eceb9fdf294175上单调递增B.eqId10852d81bc184140a7780250c82c6929eqIddca4c31f92e1447fb6eceb9fdf294175上单调递减
C.eqId10852d81bc184140a7780250c82c6929eqIddca4c31f92e1447fb6eceb9fdf294175上有极大值D.eqId10852d81bc184140a7780250c82c6929eqIddca4c31f92e1447fb6eceb9fdf294175上有极小值
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