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| Math Central | Quandaries & Queries |
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Question from Nooruddin, a student: How can I calculate the absolute minimum of (ln x)/x? |
Hi Nooruddin.
Since the domain of the function is x > 0, consider the limit as x approaches 0 from above.
- ln(x) becomes a larger and larger negative number.
- x becomes a smaller and smaller positive number.
Thus, ln(x) / x must become a larger and larger negative number as x approaches 0 from above.
So there is no absolute minimum.
Cheers,
Stephen La Rocque.
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