Hi I seem to have run into a strange problem.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose one wishes to maximize/minimize the function ## f(x) = (x-4)^{2} ##. Clearly, this function has a minimum at x = 4. One could find the extremum by taking the derivative and setting to zero.

One could also compute the logarithm of this function, i.e. ## ln (x-4)^{2} = 2 \ ln(x-4) ##, and then find the corresponding extremum of the resulting function, and since ## ln(x )## is monotonic over the region on which it is defined, the maximum/minimum of ##f(x)## and the maximum/minimum of ## f(ln(x))## should coincide.

This however is not the case, since ## 2 \ ln(x-4) ## seems not to have a maximum or a minimum. What am I missing here?

Thanks.

BiP

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# Maximum/minimum through logarithm

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