雙極值不等式證明 學(xué)生版

(1)求函數(shù)f(x)的單調(diào)區(qū)間；(2)設(shè)g(x)=f(x)+2ex+2cosx有兩個(gè)極值點(diǎn)x1，x2，且x1<x2.2.已知函數(shù)f(x)=xlnx-a(x2-1)+x.(1)討論函數(shù)f(x)的單調(diào)性；(2)若f(x)有兩個(gè)極值點(diǎn)x1，x2，求證：--x1<f<-2(-1(2.4.設(shè)函數(shù)f(x)=x(x2-3x+a)，a∈R.(1)當(dāng)a=-9時(shí)，求函數(shù)f(x)的單調(diào)增(3)若函數(shù)在區(qū)間(0,2)內(nèi)存在兩個(gè)極值點(diǎn)x1，x2，且|f(x1)-f(x2)|>|f(x1)+f(x2)|，求a的取值范圍.(2)討論函數(shù)f(x)的單調(diào)性；-ln2,-2ln2(，求a的取值范圍.6.已知函數(shù)f(x)=x2+aln(x+1).7.已知函數(shù)=alnx2-x8.x2+mx-xlnx.9.已知函數(shù)f(x)=4x-x2-alnx.(1)討論函數(shù)f(x)的單調(diào)性；(2)設(shè)函數(shù)f(x)有兩個(gè)極值點(diǎn)x1，x2(x1<x2)，證明：f(x1)+f(x2)<7+e-lnx1-lnx2.10.已知函數(shù)=alnx-(2)若函數(shù)f(x)有兩個(gè)不同的極值點(diǎn)x1，x2(x1<x2)，證明：2x2-2x1-alnx2+alnx1<0.(1)討論fl(x)的單調(diào)性(其中fl(x)是f(x)的導(dǎo)函數(shù))；(2)若函數(shù)f(x)有兩個(gè)不同的極值點(diǎn)x1，x2，13.已知函數(shù)=x2+ax-當(dāng)a=1且x>-時(shí)，求函數(shù)f(x)的單調(diào)區(qū)間；時(shí)，若函數(shù)g(x)=f(x)-x2-lnx的兩個(gè)極值點(diǎn)分別為x1，x2，證明：0<14.已知函數(shù)f(x)=x2-ax+lnx(a∈R).15.已知函數(shù)f(x)=x2-1+aln(1-x)，a∈R.16.已知函數(shù)f(x)=ex+m+(m+1)x-xlnx.17.已知函數(shù)f(x)=xlnx-ax2有兩個(gè)極值點(diǎn)x1，x2(x1<x2).18.已知f=xlnx-ax2+x有兩個(gè)極值點(diǎn)x1，x2，且x1<x2.若x2>3x11+x2>19.已知函數(shù)f(x)=x(lnx-ax)，a∈R.(1)若f(x)有兩個(gè)極值點(diǎn)x1，x2(x1<x2)．求實(shí)數(shù)a2-x1>20.已知函數(shù)f(x)=ex-ax2+e2x有兩個(gè)極值點(diǎn)x1，x2(x1<x2).21.已知函數(shù)f(x)=ex-ax2+e2x有兩個(gè)極值點(diǎn)x1，x2(x1<x2).x2<ln2a.22.已知函數(shù)f(x)=x2+ax-ex(a∈R)有兩個(gè)極值點(diǎn)x1，x2.x2<ln4.23.設(shè)函數(shù)f(x)=ae2x+(1-x)ex+a(a∈R).(2)若f(x)有兩個(gè)極值點(diǎn)x1，x2(x1<x2).24.已知函數(shù)f(x)=(x-2)ex-1-a(x-1)2.(1)求函數(shù)f(x)的極值點(diǎn)；2為g(x)=f(x)+(3-x)ex-1的兩個(gè)極值點(diǎn)，證明：x1x2<[ln(2a)+1]2.25.已知函數(shù)f(x)=mex-1-lnx，m∈R.(1)當(dāng)m≥1時(shí)，討論方程f(x)-1(i)2<x1+x2<3；(ii)g(x1)+2g(x2)<0.26.已知函數(shù)=lnx+(1)討論f(x)的單調(diào)性；(2)函數(shù)g(x)=xf(x)-ax2-x有兩個(gè)不同的極值點(diǎn)x1，x2(x1<x2)，證明：lnx1+2lnx2>28.已知函數(shù)=xlnx-x-(2)若函數(shù)f(x)有兩個(gè)不同的極值點(diǎn)x1，x2．求證：x1x2<.29.已知函數(shù)f(x)=xlnx-ax2(a∈R)在定義域內(nèi)有兩個(gè)不同的極值點(diǎn).1<x22>1.2是函數(shù)F(x)=f(x)-g(x)兩個(gè)不同的極值點(diǎn)，證明：<ln(2a).31.已知函數(shù)=xlnx-mx2-x,m∈R.(1)若g(x)=f′(x)(f′(x)為f(x)的導(dǎo)函數(shù))，求函數(shù)g(x)的單調(diào)區(qū)間；32.已知函數(shù)x2lnx-x2-ax,a∈R.34.已知函數(shù)f(x