Given the function f (x) = (A / 2) (the square of x) + 2x (a ∈ R), G (x) = LNX, if the function H (x) = g (x) - f (x) has a monotone decreasing interval, find the value range of A | Math enthusiast | Mathematical art

Given the function f (x) = (A / 2) (the square of x) + 2x (a ∈ R), G (x) = LNX, if the function H (x) = g (x) - f (x) has a monotone decreasing interval, find the value range of A

h(x)'=1/x-ax-2(x>0)
If there is no monotone decreasing interval for H (x), then H (x) is monotone increasing at (0, positive infinity)
So on (0, positive infinity)
1 / x-ax-2 > 0, that is a

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