Question 1089124
f(x) = lnx/x
:
f'(x) = (1 - ln(x)) / x^2
:
set f'(x) = 0 and solve for x
:
(1 - ln(x)) / x^2 = 0
ln(x) = 1
x = e
:
at x = e, f(x) = 1/e, this is a global maximum
:
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f(x) decreases on (e, +infinity)
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:
Here is a graph of f(x)
:
{{{ graph( 300, 200, -6, 6, -5, 5, ln(x)/x) }}}