find the maximum value of logx/x
for positive value
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Solution: (4) 1 / e
y = logx / x
dy / dx = [1 – logx] / x2
Put dy / dx = 0
[1 – logx] / x2 = 0
log x = 1
d2y / dx2 = [x2 (-1 / x) – (1 – log x) 2x] / [x2]2
At x = e, d2y / dx2 ≤ 0, maxima
The maximum value at x = e is y = log e / e = 1 / e.
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