Re: Basic plotting of an evaluated function

• To: mathgroup at smc.vnet.net
• Subject: [mg86906] Re: Basic plotting of an evaluated function
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Wed, 26 Mar 2008 04:48:36 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <fsa5cd\$ab2\$1@smc.vnet.net>

```lederer at ssb.rochester.edu wrote:

> I have some function in two varaibles
>
> f[x_,y_]= some arbitrary polynomial
>
> Now I want to minimize the function with respect to y over some
> compact interval with fixed x
>
> NMinimize[{f[x,y],y=995,y=989},y]

There are two syntax errors in the above line:

First, the expression y = 995 _assigns_ the integer value 995 to the
symbol y. What you had in mind was the comparison operator for equality,
which is written as a double equal sign == in Mathematica. (See Set, =,
and Equal, ==, and also SameQ, ===, in the online documentation.)

Second, NMinimize accepts constraints expressed in the form of
inequalities and domain specification. Therefore, your expression should

Minimize[{f[x, y], 989 <= y <= 995}, y]

> I want to plot the y's versus the x's.
>
> I have tried many things like defining
>
> s[x_]=Part[NMinimize[{f[x,y],y=995,y=989},y],2]

Using SetDelayed, :=, and the replacement operator /. should work here.

s[x_] := y /. Last@NMinimize[{f[x, y], 989 <= y <= 995}, y]

> Plot[s[x],{x,-14, 46}]

<snip>

The following expressions are a working example of what you are looking for.

f[x_, y_] := x^2 - 3 y^2 + x y + 10
s[x_] := y /. Last@NMinimize[{f[x, y], 989 <= y <= 995}, y]
Plot[s[x], {x, -14, 46}]

Hope this helps,
--
Jean-Marc

```

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