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MathGroup Archive 2007

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Re: minimum of a function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75051] Re: minimum of a function
  • From: "ahallam at iastate.edu" <ahallam at iastate.edu>
  • Date: Sun, 15 Apr 2007 05:13:13 -0400 (EDT)
  • References: <evpoqm$6cp$1@smc.vnet.net>

On Apr 14, 12:28 am, Sven Krueger <Sven-Philip.Krue... at phys.uni-
goettingen.de> wrote:
> Hi
>
> I also have a question concerning a mathematica problem:
>
> I search the minimum of a function
> fmin := FindMinimum[f[x], {x, 0}]
> Evaluate[fmin]
>
> I get out for example
> {2.4, {x -> 0.2}}
>
> Is it possible to use the result x=0.2 afterwards?
> I would like to fix x after getting out the value of x at different
> results of fmin.
>
> Thank you for your help
>
> Sven Kr=FCger

Try this.  You can pull elements from the list.

Clear[x, f, F, fmin];
f[x_] := x^4 + 4*x^3 - 50*x^2 + 84*x;
f[x]
Plot[f[x], {x, -8, 5}, AxesLabel -> {"x", "f[x]"},
   PlotStyle -> {RGBColor[0.1, 0.3, 0.8], Thickness[0.007]},
   AxesStyle -> {RGBColor[0.1, 0, 0.1], Thickness[0.01]}, ImageSize ->
600];
fmin = FindMinimum[f[x], {x, -1}];
Evaluate[fmin]
Print["This is the value of x at which f reaches a minimum"];
fminstar = fmin[[2,1,2]] (*This selects a portion of the answer*)

(*This uses Solve*)
xstar = Solve[D[f[x], x] == 0, x];
xstar
Print["This is the first critical value of f[x]"];
xstar1 = xstar[[1,1,2]]
Print["This is the second critical value of f[x]"];
xstar1 = xstar[[2,1,2]]
Print["This is the third critical value of f[x]"];
xstar1 = xstar[[3,1,2]]



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