1.

Find the maximum value of logx/xfor positive value​

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Answer:

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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