均值不等式专题讲义

1、专业好文档均值不等式专题讲义题型一、利用基本不等式求值域1、已知，求函数的最大值。2、 设，求函数的最大值 3、 求的值域。 4、求函数的值域。5、设x,y的最小值为_题型二、条件最值1、若实数满足，则的最小值是 2、已知，且，求的最小值。3、已知,且,则的最小值为4、若x,y(0,+)且2x+8y-xy=0，求x+y的最小值.5、已知正数满足，则的最小值为 6、已知a,b为正实数，且的最小值为（ 7、若正数x，y满足x+3y=5xy，则3x+4y的最小值是( )题型三、变式条件最值1、设为实数，若则的最大值是 2、若实数满足，则的最大值是3、，则的最小值 4、设正实数x,y,z满足x2-3x

2、y+4y2-z=0.则当取得最大值时，的最大值为 5、设正实数满足，则当取得最大值时，的最大值为（ ）6、设a + b = 2, b0, 则当a = 时, 取得最小值. 题型四、综合型1、若直线平分圆，则的最小值是( )2、函数，且的图象恒过定点a，若点a在直线上（其中m，n0），则的最小值等于3、已知都是正实数， 函数的图象过（0,1）点，则的最小值是4、设x，y满足约束条件 ，w.w.w.k.s.5.u.c.o.m 若目标函数z=ax+by（a0，b0）的值是最大值为12，则的最小值为( ). 5、若a0, b0, 且函数f(x)=4x3-ax2-2bx+2在x=1处有极值，则ab的最大值

3、等于（ ）6、已知a，b为正实数，2baba30，求函数y的最小值.题型五、其他情况1、设常数a0.若对一切正实数x成立，则a的取值范围为 2、已知且，求使不等式恒成立的实数的取值范围。3、若，则的大小关系是 4、已知x，y为正实数，且x 21，求x的最大值.winger tuivasa-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 fu

4、ll-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.aussie winger jarryd hayne is the competit

5、ions 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 tournament high 17 offloads - has the chanc

6、e 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 watch mcayman islands-based webb, the head

7、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 sport.for me its about how he felt and i w

8、ould 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 ordered an immediate investigation into the refe

9、rees 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 early as sunda.the weather plays an importa

10、nt 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 troposphere) where our day-to-day weather

11、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 the tropopause),e can expect a lot of turbule

12、nce.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 the same mistake against the kiwis in manches

13、ter.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 - but i have been impressed by the kangaro

14、os 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 stuff that often goes unnoticed in the stands b

15、ut 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. they have played in so many high-pressure g

16、ames - 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 bi

17、g 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-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 th

18、e encounter but australia 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 inter

19、national federation 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

20、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 watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will atte

21、nd 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 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 csk

22、afor the racist behaviour 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:

23、 we found no racist 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 preci

24、pitation or humidity 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 cr

25、uising altitude of 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

26、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 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 by 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 game