2025新高考重難點之構(gòu)造函數(shù) 學(xué)生版

1.對于不等式f/(x(>k(k≠0(，構(gòu)造函數(shù)g(x(=f(x(-kx+b2.對于不等式xf/(x(+f(x(>0，構(gòu)造函數(shù)g(x(=xf(x(3.對于不等式xf/(x(-f(x(>0，構(gòu)造函數(shù)g(x(=(x≠0(4.對于不等式xf/(x(+nf(x(>0，構(gòu)造函數(shù)g(x(=xnf(x)5.對于不等式xf/(x(-nf(x(>0，構(gòu)造函數(shù)g(x(=6.對于不等式f/(x(-f(x(>0，構(gòu)造函數(shù)g(x(=7.對于不等式f/(x(+f(x(>0，構(gòu)造函數(shù)g(x(=exf(x)8.對于不等式f/(x(+kf(x(>0，構(gòu)造函數(shù)g(x(=ekxf(x)9.對于不等式f/(x(sinx+f(x(cosx>0，構(gòu)造函數(shù)g(x(=sinxf(x)10.對于不等式f/(x(sinx-f(x(cosx>0，構(gòu)造函數(shù)g(x(=11.對于不等式f/(x(cosx-f(x(sinx>0，構(gòu)造函數(shù)g(x(=cosxf(x)12.對于不等式f/(x(cosx+f(x(sinx>0，構(gòu)造函數(shù)g(x(=1.(23-24高三下·重慶)已知函數(shù)f(x(的定義域為(-∞,0(，f(-1(=-1，其導(dǎo)函數(shù)f/(x(滿足xf/(x(-2f(x(>0，則不等式f(x+2025(+(x+2025(2<0的解集為()A.(-2026,0(B.(-2026,-2025(C.(-∞,-2026(D.(-∞,-2025(112.(2021·安徽高三月考(理))設(shè)函數(shù)f(x(是定義在(0,+∞(上的可導(dǎo)函數(shù)，其導(dǎo)函數(shù)為f'(x(，且有2f(x(>xf'(x(，則不等式4f(x-2021(>(x-2021(2f(2(的解集為()A.(2021,2023(B.(0,2022(C.(0,2020(3.(2022·四川省眉山第一中學(xué)模擬預(yù)測(理))已知可導(dǎo)函數(shù)f(x)的定義域為(0,+∞)，滿足xf/(x)-2f(x)<0，且f(2)=4，則不等式f(x)>x2的解集是.4.(23-24高三上·云南昆明則不等式f(2x(-4x2-1>0的解集為()A.(0,+∞(B.(,+∞(C.(1,+∞(D.(2,+∞(1.(22-23高三下·廣東)()A.4fC.9f((>4f(-D.9f<f(-2.(22-23高三下·廣東東莞)已知函數(shù)f(x(的定義域為(-∞,0(,其導(dǎo)函數(shù)f/(x(滿足xf/(x(-2f(x(>0,則不等式f(x+2023(-(x+2023(2f(-1(<0的解集為()A.(-2024,-2023)B.(-2024,0)C.(-∞,-2023)D.(-∞,-2024)3.(22-23高三上·山東泰安·階段練習(xí))已知f(x(是定義在R上的偶函數(shù)，f/(x(是f(x(的導(dǎo)函數(shù)，當(dāng)x≥0時，f/(x(-2x>0，且f(1(=2，則f(x(>x2+1的解集是()A.(-1,0(∪(1,+∞)B.(-∞,-1(∪(1,+∞(C.(-1,0(∪(0,1(D.(-∞,-1(∪(0,1(4.(2024·陜西商洛·模擬預(yù)測)已知函數(shù)f(x(=2xlnx-ax2，若對任意的x1,x2∈(0,+∞(，當(dāng)x1>x2時，都有2x1+f(x2(>2x2+f(x1(，則實數(shù)a的取值范圍為(),+∞(B.[1,+∞(,+∞(D.[2,+∞(5.(2023·廣東佛山·?？寄M預(yù)測)已知f/(x(是函數(shù)y=f(x((x∈R(的導(dǎo)函數(shù)，對于任意的x∈R都有f/(x(+f(x(>1，且f(0(=2023，則不等式exf(x(>ex+2022的解集是()A.(2022,+∞(B.(-∞,0(∪(2023,+∞(22C.(-∞,0(∪(0,+∞(D.(0,+∞(6.(2023·安徽黃山·統(tǒng)考三模)已知定義域為R的函數(shù)f(x(，其導(dǎo)函數(shù)為f/(x)，且滿足f/(x)-2f(x(<0，A.e2f(-1(<1B.f(1(>e2C.f<eD.f(1(>ef7.(22-23高三下·天津)已知可導(dǎo)函數(shù)f(x(的導(dǎo)函數(shù)為f/(x(,f(0(=2023，若對任意的x∈R，都有f(x(<f/(x(，則不等式f(x(<2023ex的解集為()A.(0,+∞(,+∞(C.(-D.(-∞,0(8.(22-23高三下·全國)定義域為R的可導(dǎo)函數(shù)f(x(的導(dǎo)函數(shù)為f/(x(，滿足f/(x(-f(x(<0，且f(0(A.(0,+∞(B.(2,+∞(C.(-∞,0(D.(-∞,2(1.(2023·山東煙臺·二模)已知函數(shù)f(x(的定義域為R，其導(dǎo)函數(shù)為f/(x(，且滿足f/(x(+f(x(=e-x，f(0(=0，則不等式(e2x-1(f(x(<e-的解集為().A.(-1,B.,e(C.(-1,1(D.(-1,e(2.(2022·青海西寧·二模(理))已知定義在R上的可導(dǎo)函數(shù)f(x(的導(dǎo)函數(shù)為f/(x(，滿足f/(x(<f(x(，且f(x+3(為偶函數(shù)，f(6(=1，則不等式f(x(>ex的解集為.3.(23-24高三下·廣東佛山)已知函數(shù)f(x(的定義域為(0，+∞(，且f/(x(>-f(x(ln2恒成立，則不等A.(1,e2(B.(0,e2(C.(1,e3(D.(0,e3(4.(23-24高三下·福建)設(shè)f(x)在R上存在導(dǎo)數(shù)f/(x)，滿足f/(x)+f(x)>0，且有f(2)=2,ex-2f(x)>2A.(-∞,1)B.(-∞,2)C.(1,+∞)D.(2,+∞)1.(22-23高三上·重慶沙坪壩)已知f/(x(是函數(shù)f(x(的導(dǎo)函數(shù)，f(x(-f(-x(=0，且對于任意的x∈(0,有f/(x(cosx>f(-x(sin(-x(．則下列不等式一定成立的是() 3公眾號：慧博高中數(shù)學(xué)最新試題公眾號：慧博高中數(shù)學(xué)最新試題A.f(-<f(-cosB.f(->f(-C.f(-1(<、2fcos1D.f>f(-2.(2023秋·陜西西安)已知函數(shù)f(x(的定義域為(-,，其導(dǎo)函數(shù)是f/(x(.有f/(x(cosx+f(x(sinx<0，則關(guān)于x的不等式f(x(<2fcosx的解集為()3.(22-23高三上·全國·階段練習(xí))已知函數(shù)f(x)及其導(dǎo)函數(shù)f/(x)的定義域均為(-π,0(，f(-=-2，3f(x)cosx+f/(x)sinx>0，則不等式f(x)sin3x->0的解集為()A.A.f>、2fB.f>2cos1?f(1(C.f<、2cos1?f(1(D.f<f5.(2020高三·全國·專題練習(xí))已知偶函數(shù)y=f(x)對于任意>0(其中f/(x)是函數(shù)f(x)的導(dǎo)函數(shù))，則下列不等式中不成立的是(A.、2f(-<fB.、2f(->fC.f(0)<、2f(-D.f<、3f1.(21-22高三上·江西南昌·期末)設(shè)函數(shù)f/(x(是定義在(0，π(上的函數(shù)f(x(的導(dǎo)函數(shù)，有f/(x)cosxA.a>b>cB.b>c>aC.c>a>bD.c>b>a2.(2021·東莞市東華高級中學(xué)高二期末)已知函數(shù)y=f(x)為R上的偶函數(shù)，且對于任意的x∈0,44滿足f'(x)cosx+f(x)sinx<0，則下列不等式成立的是()(>f(3.(2022·安徽·合肥一中模擬)已知函數(shù)y=f(x-1(圖象關(guān)于點(1,0(對稱，且當(dāng)x>0時，f/(x(sinx+f(x(cosx>0則