題目列表(包括答案和解析)
已知a,b是實(shí)數(shù),函數(shù)f(x)=x3+ax,g(x)=x2+bx,(x)和(x)是f(x),g(x)的導(dǎo)函數(shù),若(x)(x)≥0在區(qū)間I上恒成立,則稱f(x)和g(x)在區(qū)間I上單調(diào)性一致
(1)設(shè)a>0,若函數(shù)f(x)和g(x)在區(qū)間[-1,+∞)上單調(diào)性一致,求實(shí)數(shù)b的取值范圍;
(2)設(shè)a,b是負(fù)實(shí)數(shù),若函數(shù)f(x)和g(x)在以a,b為端點(diǎn)的開區(qū)間上單調(diào)性一致,求|a-b|的最大值.
已知a,b是實(shí)數(shù),函數(shù)f(x)=x3+ax,g(x)=x2+bx,(x)和(x)是f(x),g(x)的導(dǎo)函數(shù),若(x)(x)≥0在區(qū)間I上恒成立,則稱f(x)和g(x)在區(qū)間I上單調(diào)性一致
(1)設(shè)a>0,若函數(shù)f(x)和g(x)在區(qū)間[-1,+∞)上單調(diào)性一致,求實(shí)數(shù)b的取值范圍;
(2)設(shè)a,b是負(fù)實(shí)數(shù),若函數(shù)f(x)和g(x)在以a,b為端點(diǎn)的開區(qū)間上單調(diào)性一致,求|a-b|的最大值.
已知a,b是實(shí)數(shù),函數(shù)f(x)=x3+ax,g(x)=x2+bx,(x)和(x)是f(x),g(x)的導(dǎo)函數(shù),若(x)(x)≥0在區(qū)間I上恒成立,則稱f(x)和g(x)在區(qū)間I上單調(diào)性一致
(Ⅰ)設(shè)a>0,若函數(shù)f(x)和g(x)在區(qū)間[-1,+∞)上單調(diào)性一致,求實(shí)數(shù)b的取值范圍;
(Ⅱ)設(shè)a<0,且a≠b,若函數(shù)f(x)和g(x)在以a,b為端點(diǎn)的開區(qū)間上單調(diào)性一致,求|a-b|的最大值.
若函數(shù)f(x)對定義域中任意x均滿足f(x)+f(2a-x)=2b,則稱函數(shù)y=f(x)的圖象關(guān)于點(diǎn)(a,b)對稱.
(1)已知函數(shù)f(x)=的圖象關(guān)于點(diǎn)(0,1)對稱,求實(shí)數(shù)m的值;
(2)已知函數(shù)g(x)在(-∞,0)∪(0,+∞)上的圖象關(guān)于點(diǎn)(0,1)對稱,且當(dāng)x∈(0,+∞)時,g(x)=x2+ax+1,求函數(shù)g(x)在(-∞,0)上的解析式;
(3)在(1)(2)的條件下,當(dāng)t>0時,若對任意實(shí)數(shù)x∈(-∞,0),恒有g(shù)(x)<f(t)成立,求實(shí)數(shù)a的取值范圍.
若函數(shù)f(x)對定義域中任意x均滿足f(x)+f(2a-x)=2b,則稱函數(shù)y=f(x)的圖象關(guān)于點(diǎn)(a,b)對稱.
(1)已知函數(shù)f(x)=的圖象關(guān)于點(diǎn)(0,1)對稱,求實(shí)數(shù)m的值;
(2)已知函數(shù)g(x)在(-∞,0)∪(0,+∞)上的圖象關(guān)于點(diǎn)(0,1)對稱,且當(dāng)x∈(0,+∞)時,g(x)=x2+ax+1,求函數(shù)g(x)在(-∞,0)上的解析式;
(3)在(1)(2)的條件下,當(dāng)t>0時,若對任意實(shí)數(shù)x∈(-∞,0),恒有g(shù)(x)<f(t)成立,求實(shí)數(shù)a的取值范圍.
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