Show that the function given by fx-log x-x has maximum at x-e-

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Standard Limits to Remove Indeterminate Form

Show that the...

Question

Show that the function given byhas maximum at x = e.

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f (x) = \frac{log x}{x}

x = e

f (x) = \frac{log x - 1}{x - e}

x \neq e

x = e

f (e)

f (x) = x^{\frac{1}{x}}, (x > 0)

x = e

f (x) = \frac{e^{\frac{1}{x}} - 1}{e^{\frac{1}{x} + 1}}, if x \neq 0

= 0, if x = 0

x = 0

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