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策略1:分离参变量,构造函数求最值。分离参数法通常适用于参数与变量容易分离,并且函数的最值容易求出来的题型。通常会用到下面两个性质:(1)f(x)>a恒成立A<[f(x)]_(min);(2)f(x)[f(x)]_(max)。例1函数f(x)=x~2+2x+a/x,x∈[1,+∞),若对任意x∈[1,+∞),f(x)>0恒成立,求实数ca的取值范围。分析:若对任意x∈[1,+∞),f(x)>0恒成立,
Strategy 1: Separation of variables, the constructor to find the value. Separation parameter method is usually applied to the parameters and variables easily separated, and the function of the most easy to find the type of questions. Usually, the following two properties are used: (1) f (x)> a holds and A <[f (x)] _ (min); (2) f (x)] _ (max). Example 1 The function f (x) = x ~ 2 + 2x + a / x, x∈ [1, + ∞), and f (x)> 0 holds for any x∈ [1, + ∞) The range of ca. Analysis: For any x∈ [1, + ∞), f (x)> 0 holds,