均值不等式專題講義

1、專業(yè)好文檔均值不等式專題講義題型一、利用基本不等式求值域1、已知，求函數(shù)的最大值。2、 設(shè)，求函數(shù)的最大值 3、 求的值域。 4、求函數(shù)的值域。5、設(shè)x,y的最小值為_題型二、條件最值1、若實(shí)數(shù)滿足，則的最小值是 2、已知，且，求的最小值。3、已知,且,則的最小值為4、若x,y(0,+)且2x+8y-xy=0，求x+y的最小值.5、已知正數(shù)滿足，則的最小值為 6、已知a,b為正實(shí)數(shù)，且的最小值為（ 7、若正數(shù)x，y滿足x+3y=5xy，則3x+4y的最小值是( )題型三、變式條件最值1、設(shè)為實(shí)數(shù)，若則的最大值是 2、若實(shí)數(shù)滿足，則的最大值是3、，則的最小值 4、設(shè)正實(shí)數(shù)x,y,z滿足x2-3x

2、y+4y2-z=0.則當(dāng)取得最大值時(shí)，的最大值為 5、設(shè)正實(shí)數(shù)滿足，則當(dāng)取得最大值時(shí)，的最大值為（ ）6、設(shè)a + b = 2, b0, 則當(dāng)a = 時(shí), 取得最小值. 題型四、綜合型1、若直線平分圓，則的最小值是( )2、函數(shù)，且的圖象恒過(guò)定點(diǎn)a，若點(diǎn)a在直線上（其中m，n0），則的最小值等于3、已知都是正實(shí)數(shù)， 函數(shù)的圖象過(guò)（0,1）點(diǎn)，則的最小值是4、設(shè)x，y滿足約束條件 ，w.w.w.k.s.5.u.c.o.m 若目標(biāo)函數(shù)z=ax+by（a0，b0）的值是最大值為12，則的最小值為( ). 5、若a0, b0, 且函數(shù)f(x)=4x3-ax2-2bx+2在x=1處有極值，則ab的最大值

3、等于（ ）6、已知a，b為正實(shí)數(shù)，2baba30，求函數(shù)y的最小值.題型五、其他情況1、設(shè)常數(shù)a0.若對(duì)一切正實(shí)數(shù)x成立，則a的取值范圍為 2、已知且，求使不等式恒成立的實(shí)數(shù)的取值范圍。3、若，則的大小關(guān)系是 4、已知x，y為正實(shí)數(shù)，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