2025新高考重难点之构造函数 学生版

1.对于不等式f/(x(>k(k≠0(，构造函数g(x(=f(x(-kx+b2.对于不等式xf/(x(+f(x(>0，构造函数g(x(=xf(x(3.对于不等式xf/(x(-f(x(>0，构造函数g(x(=(x≠0(4.对于不等式xf/(x(+nf(x(>0，构造函数g(x(=xnf(x)5.对于不等式xf/(x(-nf(x(>0，构造函数g(x(=6.对于不等式f/(x(-f(x(>0，构造函数g(x(=7.对于不等式f/(x(+f(x(>0，构造函数g(x(=exf(x)8.对于不等式f/(x(+kf(x(>0，构造函数g(x(=ekxf(x)9.对于不等式f/(x(sinx+f(x(cosx>0，构造函数g(x(=sinxf(x)10.对于不等式f/(x(sinx-f(x(cosx>0，构造函数g(x(=11.对于不等式f/(x(cosx-f(x(sinx>0，构造函数g(x(=cosxf(x)12.对于不等式f/(x(cosx+f(x(sinx>0，构造函数g(x(=1.(23-24高三下·重庆)已知函数f(x(的定义域为(-∞,0(，f(-1(=-1，其导函数f/(x(满足xf/(x(-2f(x(>0，则不等式f(x+2025(+(x+2025(2<0的解集为()A.(-2026,0(B.(-2026,-2025(C.(-∞,-2026(D.(-∞,-2025(112.(2021·安徽高三月考(理))设函数f(x(是定义在(0,+∞(上的可导函数，其导函数为f'(x(，且有2f(x(>xf'(x(，则不等式4f(x-2021(>(x-2021(2f(2(的解集为()A.(2021,2023(B.(0,2022(C.(0,2020(3.(2022·四川省眉山第一中学模拟预测(理))已知可导函数f(x)的定义域为(0,+∞)，满足xf/(x)-2f(x)<0，且f(2)=4，则不等式f(x)>x2的解集是.4.(23-24高三上·云南昆明则不等式f(2x(-4x2-1>0的解集为()A.(0,+∞(B.(,+∞(C.(1,+∞(D.(2,+∞(1.(22-23高三下·广东)()A.4fC.9f((>4f(-D.9f<f(-2.(22-23高三下·广东东莞)已知函数f(x(的定义域为(-∞,0(,其导函数f/(x(满足xf/(x(-2f(x(>0,则不等式f(x+2023(-(x+2023(2f(-1(<0的解集为()A.(-2024,-2023)B.(-2024,0)C.(-∞,-2023)D.(-∞,-2024)3.(22-23高三上·山东泰安·阶段练习)已知f(x(是定义在R上的偶函数，f/(x(是f(x(的导函数，当x≥0时，f/(x(-2x>0，且f(1(=2，则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·陕西商洛·模拟预测)已知函数f(x(=2xlnx-ax2，若对任意的x1,x2∈(0,+∞(，当x1>x2时，都有2x1+f(x2(>2x2+f(x1(，则实数a的取值范围为(),+∞(B.[1,+∞(,+∞(D.[2,+∞(5.(2023·广东佛山·校考模拟预测)已知f/(x(是函数y=f(x((x∈R(的导函数，对于任意的x∈R都有f/(x(+f(x(>1，且f(0(=2023，则不等式exf(x(>ex+2022的解集是()A.(2022,+∞(B.(-∞,0(∪(2023,+∞(22C.(-∞,0(∪(0,+∞(D.(0,+∞(6.(2023·安徽黄山·统考三模)已知定义域为R的函数f(x(，其导函数为f/(x)，且满足f/(x)-2f(x(<0，A.e2f(-1(<1B.f(1(>e2C.f<eD.f(1(>ef7.(22-23高三下·天津)已知可导函数f(x(的导函数为f/(x(,f(0(=2023，若对任意的x∈R，都有f(x(<f/(x(，则不等式f(x(<2023ex的解集为()A.(0,+∞(,+∞(C.(-D.(-∞,0(8.(22-23高三下·全国)定义域为R的可导函数f(x(的导函数为f/(x(，满足f/(x(-f(x(<0，且f(0(A.(0,+∞(B.(2,+∞(C.(-∞,0(D.(-∞,2(1.(2023·山东烟台·二模)已知函数f(x(的定义域为R，其导函数为f/(x(，且满足f/(x(+f(x(=e-x，f(0(=0，则不等式(e2x-1(f(x(<e-的解集为().A.(-1,B.,e(C.(-1,1(D.(-1,e(2.(2022·青海西宁·二模(理))已知定义在R上的可导函数f(x(的导函数为f/(x(，满足f/(x(<f(x(，且f(x+3(为偶函数，f(6(=1，则不等式f(x(>ex的解集为.3.(23-24高三下·广东佛山)已知函数f(x(的定义域为(0，+∞(，且f/(x(>-f(x(ln2恒成立，则不等A.(1,e2(B.(0,e2(C.(1,e3(D.(0,e3(4.(23-24高三下·福建)设f(x)在R上存在导数f/(x)，满足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·重庆沙坪坝)已知f/(x(是函数f(x(的导函数，f(x(-f(-x(=0，且对于任意的x∈(0,有f/(x(cosx>f(-x(sin(-x(．则下列不等式一定成立的是() 3公众号：慧博高中数学最新试题公众号：慧博高中数学最新试题A.f(-<f(-cosB.f(->f(-C.f(-1(<、2fcos1D.f>f(-2.(2023秋·陕西西安)已知函数f(x(的定义域为(-,，其导函数是f/(x(.有f/(x(cosx+f(x(sinx<0，则关于x的不等式f(x(<2fcosx的解集为()3.(22-23高三上·全国·阶段练习)已知函数f(x)及其导函数f/(x)的定义域均为(-π,0(，f(-=-2，3f(x)cosx+f/(x)sinx>0，则不等式f(x)sin3x->0的解集为()A.A.f>、2fB.f>2cos1⋅f(1(C.f<、2cos1⋅f(1(D.f<f5.(2020高三·全国·专题练习)已知偶函数y=f(x)对于任意>0(其中f/(x)是函数f(x)的导函数)，则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)设函数f/(x(是定义在(0，π(上的函数f(x(的导函数，有f/(x)cosxA.a>b>cB.b>c>aC.c>a>bD.c>b>a2.(2021·东莞市东华高级中学高二期末)已知函数y=f(x)为R上的偶函数，且对于任意的x∈0,44满足f'(x)cosx+f(x)sinx<0，则下列不等式成立的是()(>f(3.(2022·安徽·合肥一中模拟)已知函数y=f(x-1(图象关于点(1,0(对称，且当x>0时，f/(x(sinx+f(x(cosx>0则