问题 解答题

已知函数f(x)=x3+x-16.

(1)求曲线y=f(x)在点(2,-6)处的切线方程;

(2)直线l为曲线y=f(x)的切线,且经过原点,求直线l的方程及切点坐标.

答案

(1)∵f'(x)=(x3+x-16)'=3x2+1,

∴在点(2,-6)处的切线的斜率k=f(2)=3×22+1=13,

∴切线的方程为y=13x-32.

(2)设切点为(x0,y0),则直线l的斜率为f'(x0)=3x02+1,

∴直线l的方程为y=(3x02+1)(x-x0)+x03+x0-16.

又∵直线l过点(0,0),∴0=(3x02+1)(-x0)+x03+x0-16,

整理,得x03=-8,∴x0=-2,∴y0=(-2)3+(-2)-16=-26,直线l的斜率k=3×(-2)2+1=13,

∴直线l的方程为y=13x,切点坐标为(-2,-26).

单项选择题 B1型题
阅读理解

阅读理解。

    The Museum of Childhood is Australia's most comprehensive collection of childhood items including

toys , dolls , infant and school material .

   Housed in a modern facility , the displays reflect Australian childhood experience over time including

play , child rearing , orphanage childhood , and home , school , and war time experience .

   There are many hands -on exhibits and education sessions including the famous 'lesson' in the 1920s

One Teacher Bush Classroom .

   The Museum also hosts national touring exhibitions and conducts special activities on Sundays and

school holidays(ring for details ).

Open: Tuesday- Friday 10am - 4pm , Sunday 10am - 4:30 pm , or by arrangement .

Special activities on Sundays as advertise .

Closed: Public holidays ,16 December-18 January .

Location: Edith Cowan University campus , Bay Road , Claremont (take bus 208 and alight at the Bay

Road and Princess Road intersection . The Museum is 15 minutes' walk from Claremont train station )

Tel :(08) 9442 1373 ; Fax ; (08 ) 9442 1314

1.On        you can stay at the Museum until half past four .

A.Wednesday

B.Friday

C.Sunday

D.Monday  

2.If you want to attend a special activity , you'd better come on           .

A.Monday

B.Tuesday

C.Saturday

D.Sunday

3.When you come on December 20th , Friday ,you will find the Museum          .

A.closed

B.holding special activities

C.not closed until 4:00

D.not closed until 4:30

4.The main purpose of the Museum of Childhood is to            .

A.display toys , dolls , infant and school material

B.reflect Australian childhood experience over time

C.host national touring exhibition      

D.tell you the famous 'lesson' in the 1920s