Just a Curiosity (to me at least) on NMaximize and FindMaximum

• To: mathgroup at smc.vnet.net
• Subject: [mg93471] Just a Curiosity (to me at least) on NMaximize and FindMaximum
• From: "Mauricio Esteban Cuak" <cuak2000 at gmail.com>
• Date: Mon, 10 Nov 2008 03:30:33 -0500 (EST)

```I was maximizing some functions and, by mistake, put a variable that I had
finally decided not to consider.Let me give you an example:

NMaximize[{-x^2 - 1, 0 <= a <= 1}, {x, a}]

Out[7]   {-1., {a -> 0.599708, x -> 0.}}

And it always chooses the same A for that functional form. If I vary the
functional form, it chooses another A:

NMaximize[{x^3 - 8 x^2, -5 <= x <= 4, 0 <= a <= 1}, {x, a}]

Out[13]   {-1.41319*10^-40, {a -> 0.66519, x -> -4.20296*10^-21}}

Why does it do that? How does it choose the A?

In a simulation I made, I obtained a plot of several maximum values for A
and tried to make an interpretation of it!

My theory for now is that the program is trying to tell me something. Or
maybe it is mocking me, I'm not sure.

```

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