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Show that the maximum value of x^1/x is e^1/e

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Show that the maximum value of x1/x is e1/e

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Best answer

The given function is Y = x1/x

Now, taking logarithm from both sides, we get..

log y = 1/x log x

Differentiating both sides w.r.t x….

(1 - ln(x)) = 0

ln(x) = 1

x = e

hence the max. point is x = e

max value is e1/e.

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