第44節(jié)導(dǎo)數(shù)之多變量不等式恒成立存在性成立上2(1)對(duì)于任意的x?,總存在x?,使得f(x?)x??f(x)max≤8(x)max'-(2)對(duì)于任意的x?,總存在x?,使得f(x?)≥g(x?)?f(x)min≥g(x)min;(3)對(duì)于任意的x1,x?,使得f(x?)≤8(x?)→f(x)ma≤8(x)min(4)若存在x?,總存在x?,使得f(x?)≤8(x?)?f(x)min≤g(x)max·上題型*題型*雙變量不等式型問題(1)對(duì)于任意的x?,總存在x?,使得f(x?)≤8(x?)?f(x)max≤8(x)max;(2)對(duì)于任意的x?,總存在x?,使得f(x?)≥8(x2)→f(x)min≥g(x)min(3)對(duì)于任意的x?,x?,使得f(x?)≤8(x2?)?f(x)max≤8(x)minf題型*題型*雙變量不等式型問題(1)對(duì)于任意的x?,總存在x?,使得f(x?)≤8(x?)?f(x)max≤8(x)max;(2)對(duì)于任意的x?,總存在x?,使得f(x?)≥8(x?)?f(x)min≥8(x)min(3)對(duì)于任意的x1,上?,使得f(x?)≤g(x?)→f(x)ma≤8(x)mn1xVA1xVAm題型*雙變量不等式型問題(1)對(duì)于任意的x?,總存在x?,使得f(x?)≤8(x2)→f(x)max≤8(x)max2(2)對(duì)于任意的x?,總存在x?,使得f(x?)≥8(x2)→f(x)mun≥8(x)mini(3)對(duì)于任意的x?,x?,使得f(x?)≤8(x?)→f(x)max≤8(x)mun(4)若存在x?,總存在x?,使得f(x?)≤8(x2)→f(x)mu≤8(x)max⑧例1修大大的數(shù)學(xué)課例1修大大的數(shù)學(xué)課(2015全國二卷理數(shù))(1)證明：f(x)在(-∞,0)單調(diào)遞減，在(0,+∞)單調(diào)遞增；-I≤m≤)(2)若對(duì)于任意x?,x?∈|-1,1],都有≤e-1,求m的取值范圍.1例1修大大的數(shù)學(xué)課例1修大大的數(shù)學(xué)課(2015全國二卷理數(shù))(1)證明：f(x)在(-∞,0)單調(diào)遞減，在(0,+∞)單調(diào)遞增；例1修大大的數(shù)學(xué)課(2015全國二卷理數(shù))(1)證明：f(x)在(-∞,0)單調(diào)遞減，在(0,+∞)單調(diào)遞增；→→mm≤-①mel-m)≤))一m≤求m的取值范圍.令修大大的數(shù)學(xué)課修大大的數(shù)學(xué)課已知函數(shù)f(%)=ax2-(2a+1)x+2Inx,g(x)=x2-2x,,,gma=g2=只Jgma=g2=只J例2修大大的數(shù)學(xué)課若對(duì)任意的x若對(duì)任意的x?∈(0,2),△Q7n2-1.下C例2已知函數(shù),g(x)=x2-2x,若對(duì)任意的x?∈(0,2),均存在x?∈(0,2),使得f(x?)<g(x?),求a的取值范圍.a7n2-1.10②a=0時(shí)f(x=)=②a=0時(shí)f(x=)=土fcou土fcou)↓(I))求b范圍.求b范圍.hix)hin≤2.略一一Xt例4修大大的數(shù)學(xué)課★(2019廣東東莞期末)例4修大大的數(shù)學(xué)課★(2019廣東東莞期末)業(yè)個(gè)a人★處取得極值.a》了函數(shù)g(x)=a2x2+3,若存在m?,3<a<4.使得立，求a的取值范圍.3<a<4.③a22土f=Lb(7,0-1)個(gè)A11)修大大的數(shù)學(xué)課Ah=1-QX)=)修大大的數(shù)學(xué)課(1)若a>1,求函數(shù)f(x)的單調(diào)區(qū)間；3<Q<4.↓0gmy>fou→gmy>fou→gIm2zf0l1)修大大的數(shù)學(xué)課##數(shù)量.)成立，求m范圍.工工a→四四x上恒增；①①Rm≥.例6例6上恒增；mxexx人x十山h1X):[2.2)一h1X):[2.2)一一一上恒增；m(2)Va∈(1,2),mm年mf(x)≥bx-2恒成立，求b范圍.b≤2修大大的數(shù)學(xué)課一て1.P1)+