2024学生版大二轮数学新高考提高版（京津琼鲁辽粤冀鄂湘渝闽苏浙黑吉晋皖云豫新甘贵赣桂）专题一　第5讲　母题突破2　恒成立问题与能成立问题14

这是一份2024学生版大二轮数学新高考提高版（京津琼鲁辽粤冀鄂湘渝闽苏浙黑吉晋皖云豫新甘贵赣桂）专题一　第5讲　母题突破2　恒成立问题与能成立问题14，共3页。
思路分析一
❶fx≥0恒成立
❷fxmin≥0
❸分类讨论求fxmin
思路分析二
❶fx≥0恒成立
❷求证x－ln x>0
❸分离参数构造新函数
❹求新函数最值
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[子题1] (2023·青岛模拟)已知函数f(x)＝ex－a－ln x．若存在x0∈[e，＋∞)，使f(x0)f(x)max或a－1.若存在x1∈[1,3]，对任意的x2∈[e2，e3]，使得不等式g(x2)>f(x1)成立，求实数a的取值范围．(e3≈20.09)
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2．(2023·全国甲卷)已知函数f(x)＝ax－eq \f(sin x,cs3x)，x∈eq \b\lc\(\rc\)(\a\vs4\al\c1(0，\f(π,2))).
(1)当a＝8时，讨论f(x)的单调性；
(2)若f(x)