# Maximise over functions in Mathematica

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.

Assuming you have a particular point (x,y,z) in mind:
MaximalBy[{h,j,k},#[x,y,z]&]

• 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? – Sid Dec 4 '19 at 10:06
• @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. – Alan Dec 4 '19 at 14:10