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河北省张家口市宣化区第四中学2015-2016学年高二数学文寒假作业15

寒假作业 15(文科)(选修 1--1) 第三章 导数及其应用
一、选择题 1. y ? x 在 x ? 1 处的导数为(
2

) C.2 D.1

A. 2 x

B.2 ? ?x

2.下列求导数运算正确的是(


'

1 1 ( x ? )' ? 1 ? 2 x x A.

1 (3x ) ' ? 3x log3 e D. ( x 2 cos x) ' ? ?2x sin x B. (log2 x) ? x ln 2 C.

3. .函数 y ? 3x ? x 的单调增区间是(
3

) C.(-1,1) D.(1,+∞)

A.(0,+∞)

B.(-∞,-1)
2

4.函数 f(x)=x (1 ? x) 有 ( A 0 B 1 C 2
3

)个极值点。 D 3

5. 三次函数 f ( x) ? ax ? 2 x +5 在 x ? (??,??) 内是增函数,则( A. a >0 B. a <0 C. a =1 D. a = 3
1



3 2 6.与直线 3x ? y ? 8 ? 0 平行的曲线 y ? x ? 3x ? 1的切线方程为(



(A) y ? 3x ? 4 (B) y ? ?3x ? 2

(C) y ? ?4 x ? 3

(D) y ? 4 x ? 5

二、填空题 7. 曲线 y ? x ? 3x 在点 P(?2, ?14) 处的切线方程是
3



4 3 2 (1 , 0) f ( x ) ? x ? px ? qx 8..函数 的图象与 x 轴相切于点 ,极大值为 27 ,则极小值为
2 9..函数 y ? 2x ? ln x( x ? 0) 的单调增区间为



三、解答题 3 2 3 10.已知函数 f(x)=ax - x +1(x∈R),其中 a>0. 2 (1)若 a=1,求曲线 y=f(x)在点(2,f(2))处的切线方程; 1 1 (2)若在区间[- , ]上,f(x)>0 恒成立,求 a 的取值范围. 2 2

高二数学错题总结


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