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Define the functions $h$, $j$, and $k$ that are each functions of 3 variables:

h[x,y,z]
j[x,y,z]
k[x,y,z]

How can I find the max of these functions? I want the answer to return the function which is the largest.

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Assuming you have a particular point (x,y,z) in mind:

MaximalBy[{h,j,k},#[x,y,z]&]
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  • $\begingroup$ indeed for a particular point (x,y,z). How can I also return the element in the set {h,j,k} that corresponds to the Maximum? $\endgroup$ – Sid Dec 4 '19 at 10:06
  • $\begingroup$ @Sid That's an entirely different question. Define m[x_,y_,z_]:=Max[h[x,y,z],j[x,y,z],k[x,y,z]] and then apply FindMaximum. $\endgroup$ – Alan Dec 4 '19 at 14:10

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