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Simple question from a beginner: I seem to be unable to do maximization if the variable has a power specified symbolically instead of numerically?

Maximize[-x^2+a*x,x]

But now:

Maximize[-x^b+a*x,x] 

Seems to fail. Am I doing something wrong? Or can indeed Mathematica no maximize symbolically, at least with powers? Are there other cases it will fail?

And last question, does this imply I should code manually, solving the FOCs by hand?

Thanks!

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  • $\begingroup$ You are making assumptions on b that are not necessarily the same as Mathematica; e.g. it assumes everything is complex-valued unless explicitly told otherwise. $\endgroup$ Commented Apr 4, 2016 at 0:38

1 Answer 1

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It is because there is no general solution for your problem, even for b being a positive integer: When b is odd, the maximum is positive infinity, while for even b it is not. You may want to use things like Maximize[-x^# + a*x, x] & /@ Table[i, {i, 5}] to observe.

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  • $\begingroup$ Sure, makes full sense, thanks!! This leads me to the more precise question: how can I specify the range of my "parameters" (as opposed to arguments of the function) a and b? Here I had b between 0 and 1, and a >0? As an example, I tried Maximize[{x^0.5 - a*x, x > 0, a > 0}, x] but this didn't seem to work... Thanks so much! $\endgroup$
    – Matifou
    Commented Apr 4, 2016 at 3:10
  • $\begingroup$ @Matifou I recommend that you post a new question, rather than trying to add more material to the original question by meant of comments. $\endgroup$
    – bbgodfrey
    Commented Apr 4, 2016 at 4:23

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