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So I was just messing around with finding the maximum and minimum values of functions, and I came across this:

$$ \text{Find the maximum value of} \,\, f(x)=\frac1{x^{2x^2}}.$$

Any ideas?

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  • $\begingroup$ what domain? there are several ways how one could approach this problem, one is certainly to study the derivative - you could also start by plotting the function and get some intuition $\endgroup$
    – user190080
    May 1 '16 at 10:45
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Hint. Assume $x>0$. Then you get $$ f'(x)=\frac{-2x\times (1+2 \ln x)}{x^{2 x^2}} . $$ Can you take it from here?

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  • $\begingroup$ Oops, looks like I made a blunder in differenciating the function. Stupid. Thanks :) $\endgroup$
    – b_boundary
    May 1 '16 at 10:54
  • $\begingroup$ You are welcome. $\endgroup$ May 1 '16 at 10:58

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