The maximum of function f (x) = (a + LNX) / X (a ∈ R) is equal to? The function f (x) = (a + LNX) / X (a ∈ R) is known, (1) How to find the extremum of function f (x)? (2) If a > 1, prove that there exists x0 belonging to (0, + infinity), such that f (x0) > A? thank you

The maximum of function f (x) = (a + LNX) / X (a ∈ R) is equal to? The function f (x) = (a + LNX) / X (a ∈ R) is known, (1) How to find the extremum of function f (x)? (2) If a > 1, prove that there exists x0 belonging to (0, + infinity), such that f (x0) > A? thank you

(1) ∵ function f (x) = (a + LNX) / X (a ∈ R) ∵ if f '(x) = [1 - (a + LNX)] / x ^ 2, Let f' (x) = 0, then [1 - (a + LNX)] / x ^ 2 = 0, that is, 1 - (a + LNX) = 0x = e ^ (1-A) ∵ when x = e ^ (1-A), the minimum value f (x) = f [e ^ (1-A)] = [a + lne ^ (...)