导数讲义 2.doc

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1、1、ABC的内角A,B,C的对边分别为a,b,c,已知a=bcosC+csinB.(1)求B.(2)若b=2,求ABC面积的最大值.2、设锐角三角形的内角的对边分别为，（）求的大小；（）求的取值范围导数讲义（二）一、导函数与单调性题型一、利用导数求单调区间1、判断下列函数的单调性，并求出单调区间（1）； （2）（3）； （4）2、求下列函数的单调区间1.f(x)=2x36x2+7 2.f(x)=+2x 3. f(x)=sinx , x 4. y=xlnx3、设f(x)=x2(2-x),则f(x)的单调增区间是 （ ）A.(0, B.(+) C.(-,0) D.(-,0)(,+）4、函数y=(x

2、+1)(x21)的单调递增区间为（） A.(-,1) B.（1,+） C. (-,1) 与（1,+） D. (-,1) （1,+）5、函数是减函数的区间为（ ）A B C D（0，2）6、函数的单调递增区间是( )A. B.(0,3) C.(1,4) D. 7、函数的单调减区间为 题型二：基础取值范围1、若函数f(x)=x3-ax2+1在（0，2）内单调递减，则实数a的取值范围为 2、设在上是单调函数. 则实数的取值范围为 ；3、函数y=ax3x在(,+)上是减函数，则实数的取值范围为 ；4、若函数f（x）=ax3x2+x5在R上单调递增，则a的范围是 5、已知函数在R上是减函数，则的取值范围

3、是： 6、若在R上是增函数，则（ ）（A） （B） （C） （D）7、函数在上为减函数，在上为增函数，则（ ）（A） （B） （C） （D）过渡题设函数，其中常数a1()讨论f(x)的单调性;二极值1、函数的极大值，极小值分别是 A. 极小值-1，极大值1 B. 极小值-2，极大值3 C. 极小值-2，极大值2 D. 极小值-1，极大值32函数，已知在时取得极值，则=（ ）（A）2（B）3（C）4（D）53.函数f(x)=x3-ax2-bx+a2,在x=1时有极值10，则a、b的值为 （ ）A.a=3,b=-3，或a=-4,b=11 B.a=-4,b=11C.a=3,b=-3 D.以上都不正确

4、4、已知函数的导数为，且图象过点（0，-5），当函数取得极大值-5时，x的值应为 A. 1 B. 0 C. 1 D. 15.若函数f(x)=x3-3bx+3b在（0，1）内有极小值，则 （ ）A.0b1 B.b0 D.b6.若f(x)=x3+3ax2+3(a+2)x+1没有极值，则a的取值范围为 .7. 已知函数y=2x3+ax2+36x24在x=24处有极值，则该函数的一个递增区间是（）A.(2,3) B.(3, +) C.(2, +) D. (,3)8.（2009辽宁卷文）若函数在处取极值，则 三最值1函数在0，3上的最大值、最小值分别是 （ ）A5，15B5，4C4，15D5，162.（

5、06浙江文）在区间上的最大值是（ ）(A)-2 (B)0 (C)2 (D)43函数y=x3+在(0，+)上的最小值为A.4B.5C.3D.14（07湖南理）函数在区间上的最小值是 5（07江苏）已知函数在区间上的最大值与最小值分别为，则_变式、函数在区间上的最大值、最小值分别为M，N，则MN的值为 。6.（2008安徽文）设函数 则（ ）A有最大值 B有最小值 C是增函数D是减函数四、导数图象1、函数在定义域内可导，其图象如图，记的导函数为，则不等式的解集为_ 2、函数的定义域为开区间，导函数在内的图象如图所示，则函数的单调增区间是_1. 如图为函数的图象，为函数的导函数，则不等式的解集为_

6、_ 3、若函数的图象的顶点在第四象限，则其导函数的图象是（ ）O12xyO12xyxyyO12yO12xO12xABCD4、 设是函数的导函数,的图象如右图所示，则的图象最有可能的是（）5、设函数f(x)在定义域内可导，y=f(x)的图象如下左图所示，则导函数y=f (x)的图象可能为6、 函数的图像如下右图所示，则的图像可能是（ ）xoy7、 已知函数的导函数的图象如右图，则的图象可能是( ) 8、已知二次函数的图象如图1所示 , 则其导函数的图象大致形状是（ ）9、若函数的导函数在区间上是增函数，则函数在区间上的图象可能是 ( )yababaoxoxybaoxyoxybA B C D10、

7、如果函数的图象如右图，那么导函数的图象可能是( )11、已知函数y=f(x),y=g(x)的导函数的图象如下图，那么y=f(x),y=g(x)的图象可能是（ ） 12、设是函数的导函数，将和的图像画在同一个直角坐标系中，不可能正确的是（ ）ABCDxyx4OoO13、已知函数的导函数的图像如下，则（ ）函数有1个极大值点，1个极小值点函数有2个极大值点，2个极小值点函数有3个极大值点，1个极小值点函数有1个极大值点，3个极小值点14、函数的定义域为，其导函数内的图象如图所示，则函数在区间内极小值点的个数是（ ）(A).1 (B).2 (C).3 (D).4待添加的隐藏文字内容2Winger T

8、uivasa-Sheck, who scored two tries in the Kiwis 20-18 semi-final win over England, has been passed fit after a lower-leg injury, while Slater has been named at full-back but is still recovering from a knee injury aggravated against USA.Both sides boast 100% records heading into the encounter but Aus

9、tralia have not conceded a try since Josh Charnleys effort in their first pool match against England on the opening day.Aussie winger Jarryd Hayne is the competitions top try scorer with nine, closely followed by Tuivasa-Sheck with eight.But it is recently named Rugby League International Federation

10、 player of the year Sonny Bill Williams who has attracted the most interest in the tournament so far.The Kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the World Cup in both rugby league and rugby union after triumphing with the All Blacks in 2011.Id g

11、ive every award back in a heartbeat just to get across the line this weekend, said Williams.The (lack of) air up there Watch mCayman Islands-based Webb, the head of Fifas anti-racism taskforce, is in London for the Football Associations 150th anniversary celebrations and will attend Citys Premier Le

12、ague match at Chelsea on Sunday.I am going to be at the match tomorrow and I have asked to meet Yaya Toure, he told BBC Sport.For me its about how he felt and I would like to speak to him first to find out what his experience was.Uefa hasopened disciplinary proceedings against CSKAfor the racist beh

13、aviour of their fans duringCitys 2-1 win.Michel Platini, president of European footballs governing body, has also ordered an immediate investigation into the referees actions.CSKA said they were surprised and disappointed by Toures complaint. In a statement the Russian side added: We found no racist

14、 insults from fans of CSKA. Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunda.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidit

15、y and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of

16、commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet ( Then, I would assume, he will slowly step out onto something rese

17、mbling an Olympic diving platform.They blew it in 2008 when they got caught cold in the final and they will not make the same mistake against the Kiwis in Manchester.Five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored b

18、y Englands Josh Charnley in the opening game of the tournament.That could be classed as a weakness, a team under-cooked - but I have been impressed by the Kangaroos focus in their games since then.They have been concentrating on the sort of stuff that wins you tough, even contests - strong defence,

19、especially on their own goal-line, completing sets and a good kick-chase. Theyve been great at all the unglamorous stuff that often goes unnoticed in the stands but not by your team-mates.It is as though their entire tournament has been preparation for the final.In Johnathan Thurston, Cooper Cronk,

20、Cameron Smith and either Billy Slater or Greg Inglis at full-back they have a spine that is unmatched in rugby league. They have played in so many high-pressure games - a priceless asset going into Saturday.The Kiwis are a lot less experienced but winning a dramatic match like their semi-final again

21、st England will do wonders for their confidence.They defeated Australia in the Four Nations final in 2010 and the last World Cup, and know they can rise to the big occasion.Winger Tuivasa-Sheck, who scored two tries in the Kiwis 20-18 semi-final win over England, has been passed fit after a lower-le

22、g injury, while Slater has been named at full-back but is still recovering from a knee injury aggravated against USA.Both sides boast 100% records heading into the encounter but Australia have not conceded a try since Josh Charnleys effort in their first pool match against England on the opening day

23、.Aussie winger Jarryd Hayne is the competitions top try scorer with nine, closely followed by Tuivasa-Sheck with eight.But it is recently named Rugby League International Federation player of the year Sonny Bill Williams who has attracted the most interest in the tournament so far.The Kiwi - with a

24、tournament high 17 offloads - has the chance of becoming the first player to win the World Cup in both rugby league and rugby union after triumphing with the All Blacks in 2011.Id give every award back in a heartbeat just to get across the line this weekend, said Williams.The (lack of) air up there

25、Watch mCayman Islands-based Webb, the head of Fifas anti-racism taskforce, is in London for the Football Associations 150th anniversary celebrations and will attend Citys Premier League match at Chelsea on Sunday.I am going to be at the match tomorrow and I have asked to meet Yaya Toure, he told BBC

26、 Sport.For me its about how he felt and I would like to speak to him first to find out what his experience was.Uefa hasopened disciplinary proceedings against CSKAfor the racist behaviour of their fans duringCitys 2-1 win.Michel Platini, president of European footballs governing body, has also order

27、ed an immediate investigation into the referees actions.CSKA said they were surprised and disappointed by Toures complaint. In a statement the Russian side added: We found no racist insults from fans of CSKA. Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as

28、early as Sunda.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the

29、 troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called th

30、e tropopause),e can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet ( Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.They blew it in 2008 when they got caught cold in the final and they will not make th

31、e same mistake against the Kiwis in Manchester.Five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by Englands Josh Charnley in the opening game of the tournament.That could be classed as a weakness, a team under-cooked

32、 - but I have been impressed by the Kangaroos focus in their games since then.They have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets and a good kick-chase. Theyve been great at all the unglamorous stuf

33、f that often goes unnoticed in the stands but not by your team-mates.It is as though their entire tournament has been preparation for the final.In Johnathan Thurston, Cooper Cronk, Cameron Smith and either Billy Slater or Greg Inglis at full-back they have a spine that is unmatched in rugby league.

34、They have played in so many high-pressure games - a priceless asset going into Saturday.The Kiwis are a lot less experienced but winning a dramatic match like their semi-final against England will do wonders for their confidence.They defeated Australia in the Four Nations final in 2010 and the last World Cup, and know they can rise to the big occasion.