Find minimum or maximum of multi-variable function

[jte]

One thing I didn’t realize until recently is that there certainly is a possibility of a bit of ambiguity in “find the minimum or maximum of…“. I was assuming the location of the extrema was wanted (whereas I’d think it the value of the extrema that was wanted if “find the minimum or maximum value of…” were the expression used). And, conversely, to clarify that it’s the location that’s wanted something like “find the location of the minimum or maximum value of…” could be employed. I’m not sure if there’s patterns in how different people interpret it. (I’m guessing it depends on things like textbooks read and classes attended…)

(08-28-2019 05:29 PM)roadrunner Wrote:  If you plot the equation n the 3D app:

sqrt((X-14)^2+(Y-55)^2)+sqrt((X-23)^2+(Y-95)^2)
⋮

One way to empirically check (non-rigorously) how a value relates to a function is to add a level plane to the plot (add FZ(X,Y)=K for a chosen constant K), as shown by these screenshots:

           

The first and second have a plane at Z=41 added. Peeking beneath doesn’t show any of the function falling below Z=41. For the third, I’ve raised the plane to Z=41.5 and now see a little bit of the surface dropping beneath the horizontal plane.