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21-11-2016
Mathematics

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Maximum value of (log x)/x

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HomertheGenius HomertheGenius

24-11-2016

y = log x / x
y ` = (( log x )` * x - (x)` * log x) / x²=
= (1/x * x - 1 * log x ) / x² =
= ( 1 - log x ) / x²
y ` = 0;
1 - log x = 0
log x = 1
x = e
The maximum value:
y max = log e / e = 1 / e

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