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+1 vote
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in Derivatives by (29.4k points)
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Write the minimum value of f(x) = x1/x .

1 Answer

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Best answer

Let y = x(\(\frac{1}{x}\)).

Take antilog on both sides,

⇒ In y = \(\frac{1}{x}\) \(\times\) In x

Let us differentiate and find f’(x) = 0

But In x is not defined at x = 0

f(e) = e\(\frac{1}{e}\)

Therefore, 

Minima occur at  x = e.

So, 

f(e) = e\(\frac{1}{e}\) is the minimum value of this function.

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