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I have a function of six variables, a known function, say y= F(x1, x2, x3, x4, x5, x6). I know the ranges of these variables: a1<x1<b1, a2<x2<b2, a3<x3<b3, a4<x4<b4, a5<x5<b5, a6<x6<b6. Is it possible to figure out whether a certain value of this function is reached for any set of the variables. I suspect that a certain value of y, say y0=10^{-12} can be achieved for at least one set of variables x1, x2, x3, x4, x5, x6. is it possible to find this set in Mathematica?

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    $\begingroup$ It would help if you give the function and ranges. $\endgroup$
    – David G. Stork
    Commented Nov 30, 2022 at 3:35
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    $\begingroup$ Please post your Mathematica code. $\endgroup$
    – cvgmt
    Commented Dec 14, 2022 at 0:50
  • $\begingroup$ You could try ContourPlot and Manipulate. For example, see my answer mathematica.stackexchange.com/a/277272/86543 $\endgroup$
    – userrandrand
    Commented Dec 14, 2022 at 5:43

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I would try:

Assuming[{a1<x1<b1, ...},
FindInstance[f(x1,...,x6) == desiredValue, {x1,...,x6}]]

If you give us your full problem (with details), we can better help you.

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  • $\begingroup$ thank you David. This works but takes too much time. Is there a way that I can use to speed up the process? Can a new command be added to the already existing ones to achieve this goal? $\endgroup$
    – neutrino
    Commented Dec 1, 2022 at 17:54
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    $\begingroup$ @neutrino: Why oh why do you need a new command?? The several hours it would take you to write and debug the code is MUCH longer than simply typing the above. $\endgroup$
    – David G. Stork
    Commented Dec 16, 2022 at 0:27

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