FindRoot solved

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg472] FindRoot solved
• From: Chengri Ding <ding at gis.uiuc.edu>
• Date: Tue, 14 Feb 1995 15:02:40 -0600

```Thanks for the listed people who help to solve my problem I posted a couple days ago.

Michael Trott
Wolfram Research, Inc.

Fredrick I. Olness
Internet:   Olness at phyvms.physics.smu.edu (129.119.200.74)
Olness at mail.physics.smu.edu

Thx you for your help. I, fortunately solved the problem by using FindRoot command rather than NSovle after reformuling and correting somepart. But I still can
not use FindMinimum to get the same solution. I hope you can help me figure out
what is wrong.

Ojective function is:

-(k/E^(0.01*t)) + 0.6425702811245005*t - 0.0963855421686749*t^2 +
0.004819277108433735*t^3 + (3.375333333333331*10^7 +
5.001999999999999*10^6*k + 247050.*k^2 + 4066.666666666667*k^3 -
5533.333333333352*t - 820.000000000003*k*t - 40.50000000000017*k^2*t -
0.6666666666666691*k^3*t + 830.000000000002*t^2 +
123.0000000000003*k*t^2 + 6.075000000000017*k^2*t^2 +
0.1000000000000002*k^3*t^2 - 41.50000000000001*t^3 -
6.150000000000002*k*t^3 - 0.3037500000000002*k^2*t^3 -
0.005000000000000001*k^3*t^3)/
(8611.25 + 1260.5625*k + 61.50000000000001*k^2 + 1.*k^3)

two first derivative function is

1:

(1.818989403545856*10^-12*E^(0.01*t) + 86.1125*k - 10.*E^(0.01*t)*k +
12.605625*k^2 - 0.981927710843394*E^(0.01*t)*k^2 +
0.6150000000000001*k^3 - 0.02409638554216864*E^(0.01*t)*k^3 +
0.01*k^4 + 3.000000000000085*E^(0.01*t)*k*t +
0.2945783132530213*E^(0.01*t)*k^2*t +
0.007228915662650688*E^(0.01*t)*k^3*t +
1.4210854715202*10^-14*E^(0.01*t)*t^2 -
0.2250000000000014*E^(0.01*t)*k*t^2 -
0.02209337349397633*E^(0.01*t)*k^2*t^2 -
0.0005421686746987959*E^(0.01*t)*k^3*t^2)/
(E^(0.01*t)*(8611.25 + 1260.5625*k + 61.50000000000001*k^2 + 1.*k^3))

2:
(-(7.415362656250001*10^7) + 5.252862500000154*10^8*E^(0.01*t) -
2.171003765625*10^7*k + 1.031586250000038*10^8*E^(0.01*t)*k -
2.64820156640625*10^6*k^2 + 7.596215625000001*10^6*E^(0.01*t)*k^2 -
172271.6875*k^3 + 248575.0000000149*E^(0.01*t)*k^3 - 6303.375*k^4 +
3050.*E^(0.01*t)*k^4 - 123.*k^5 +
1.818989403545856*10^-12*E^(0.01*t)*k^5 - 1.*k^6 -
86112.5000000028*E^(0.01*t)*t - 16911.25000000047*E^(0.01*t)*k*t -
1245.281250000058*E^(0.01*t)*k^2*t -
40.75000000000183*E^(0.01*t)*k^3*t -
0.5000000000000285*E^(0.01*t)*k^4*t -
4.440892098500627*10^-16*E^(0.01*t)*k^5*t +
12916.87500000035*E^(0.01*t)*t^2 + 2536.687500000058*E^(0.01*t)*k*t^2 +
186.7921875000065*E^(0.01*t)*k^2*t^2 +
6.112499999999728*E^(0.01*t)*k^3*t^2 +
0.07499999999999929*E^(0.01*t)*k^4*t^2 -
645.8437500000074*E^(0.01*t)*t^3 - 126.834375000004*E^(0.01*t)*k*t^3 -
9.33960937500024*E^(0.01*t)*k^2*t^3 -
0.3056250000000134*E^(0.01*t)*k^3*t^3 -
0.00374999999999992*E^(0.01*t)*k^4*t^3)/
(E^(0.01*t)*(8611.25 + 1260.5625*k + 61.50000000000001*k^2 + 1.*k^3)^2)

and then I used FindRoot[{equ1==0,equ2==0},{t,50},{k,150}]
got solution:

{t -> 35.6386, k -> 44.2428}

But I cannot get solution by  FindMinimum[test3[t,k],{t,35},{k,44}]
The message is: FindMinimum::fmlim: The minimum could not be bracketed in 30 iterations.

Appreciate for your any further help.

chengri Ding
University of Illinois at Urbana-Champaign

```

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