Given the function f (x) = LNX + X & # 178; + ax (a ∈ R), if the function FX is an increasing function in its domain of definition, find the value range of A

Given the function f (x) = LNX + X & # 178; + ax (a ∈ R), if the function FX is an increasing function in its domain of definition, find the value range of A

According to the title, we know that if x > 0 and f (x) derivative is 1 / x + 2x + A, the function f (x) is required to be an increasing function in its domain of definition, then 1 / x + 2x + A is required. In the case of x > 0, it is always greater than 0, that is, the minimum value is greater than 0, G (x) = 1 / x + 2x + A, and its derivative is - 1 / X & # 178; + 2, then the extreme point x = 1 / √ 2, G (1 / √ 2) > 0, then a > - 2 √ 2