Re: rootsearch in a piecewise function

• To: mathgroup at smc.vnet.net
• Subject: [mg60254] Re: rootsearch in a piecewise function
• From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
• Date: Thu, 8 Sep 2005 06:37:20 -0400 (EDT)
• Organization: Uni Leipzig
• References: <dfovrd\$feo\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

because you don't define a Picewise[] function
para = {a -> 3, b -> 4, c -> 20, d -> 1.5};
f2[x_] := 10 + a* x^(1/2) - x - b;
f3[x_] := -6 + c/x + d^2;
f1[x_] := Piecewise[{{ f2[x], 0 < x < b},

{ f3[x], b <= x < 10},

{ x^(1/2), 10 <= x}}] /.
para;

df1[x_] = D[f1[x], x];

FindRoot[Evaluate[{f1[x] == 0} /. para], {x, 2}]
FindRoot[Evaluate[{df1[x] == 0} /. para], {x, 2}]

work as expected.

Regards

Jens

"juejung" <juejung at indiana.edu> schrieb im
Newsbeitrag news:dfovrd\$feo\$1 at smc.vnet.net...
| hi group,
|
| why does the root search in the following
piecewise function not work,
| when the plot function before evaluates just
fine.
| if i use the /.para already at the point where i
define f2 and f3 then the
| root command works. however, the actual
functions f2 and f3 are much
| longer and i would like to replace
parametervalues only at the point where
| i do in the example below. it seems that
findroot is evaluated before the
| replacement takes place??
|
| thanks
| juergen
|
| para = {a -> 3, b -> 4, c -> 20, d -> 1.5};
| f2[x_] := 10 + a* x^(1/2) - x - b;
| f3[x_] := -6 + c/x + d^2;
| f1[x_] := Which[0 < x < b, f2[x], b <= x < 10,
f3[x],10 <= x, x^(1/2)]
| /.para;
| df1[x_] = D[f1[x], x];
|
| Plot[f1[x] /.para, {x, 0.1, 15}]
| Plot[df1[x] /.para, {x,0.1, 15}]
|
| FindRoot[{f1[x] == 0} /.para, {x, 2}]
| FindRoot[{df1[x] == 0} /.para, {x, 2}]
|

```

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