Let f (x) = LNX / X. if f (x) = A / X - f (x). A belongs to R. find the minimum of F (x)

Let f (x) = LNX / X. if f (x) = A / X - f (x). A belongs to R. find the minimum of F (x)

A:
f(x)=lnx/x
F(x)=a/x-f(x)
=a/x-lnx/x
=(a-lnx)/x
x>0
Derivation of F (x): F '(x) = - 1 / x ^ 2 - (a-lnx) / x ^ 2 = (lnx-a-1) / x ^ 2
The solution f '(x) = 0 is: lnx-a-1 = 0, x = e ^ (a + 1)
When 00, f (x) is an increasing function
So: when x = e ^ (a + 1), f (x) has a minimum [a - (a + 1) / e ^ (a + 1) = - e ^ (- A-1)

Elden Ring Premiere

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