plot solution derivative

[Beata Warchoł]

Dear Math Group,

I need your help in this problem:

I have date and function for example:
date= {{39814.`, 876.34`}, {39817.`, 859.91`}, {39818.`,
864.55`}, {39819.`, 840.95`}, {39820.`, 853.95`}, {39821.`,
856.52`}, {39824.`, 823.25`}, {39825.`, 821.24`}, {39826.`,
810.06`}, {39827.`, 812.87`}, {39828.`, 839.28`}, {39831.`,
836.`}, {39832.`, 852.53`}, {39833.`, 852.08`}, {39834.`,
860.32`}, {39835.`, 895.88`}, {39838.`, 906.7`}, {39839.`,
899.07`}, {39840.`, 890.05`}, {39841.`, 904.5`}, {39842.`,
928.08`}, {39845.`, 904.93`}, {39846.`, 892.93`}, {39847.`,
901.3`}, {39848.`, 913.9`}, {39849.`, 913.3`}, {39852.`,
894.15`}, {39853.`, 913.1`}, {39854.`, 942.38`}, {39855.`,
951.3`}, {39856.`, 939.76`}, {39859.`, 943.24`}, {39860.`,
969.7`}, {39861.`, 980.11`}, {39862.`, 974.3`}, {39863.`,
997.37`}, {39866.`, 993.84`}, {39867.`, 967.23`}, {39868.`,
963.28`}, {39869.`, 938.99`}, {39870.`, 938.96`}, {39873.`,
937.42`}, {39874.`, 913.28`}, {39875.`, 905.04`}, {39876.`,
927.08`}, {39877.`, 940.1`}, {39880.`, 916.36`}, {39881.`,
897.09`}, {39882.`, 906.94`}, {39883.`, 923.36`}, {39884.`,
928.13`}, {39887.`, 922.62`}, {39888.`, 916.33`}, {39889.`,
932.7`}, {39890.`, 956.68`}, {39891.`, 952.94`}, {39894.`,
950.66`}, {39895.`, 929.5`}, {39896.`, 935.54`}, {39897.`,
938.41`}, {39898.`, 922.8`}, {39901.`, 915.86`}, {39902.`,
922.58`}, {39903.`, 925.`}, {39904.`, 906.56`}, {39905.`,
895.91`}, {39908.`, 869.9`}, {39909.`, 882.11`}, {39910.`,
883.84`}, {39911.`, 881.65`}, {39915.`, 891.4`}, {39916.`,
890.6`}, {39917.`, 891.25`}, {39918.`, 878.05`}, {39919.`,
866.59`}, {39922.`, 884.35`}, {39923.`, 881.05`}, {39924.`,
891.3`}, {39925.`, 905.46`}, {39926.`, 911.8`}, {39929.`,
907.14`}, {39930.`, 891.05`}, {39931.`, 899.57`}, {39932.`,
890.85`}, {39933.`, 885.5`}, {39936.`, 901.7`}, {39937.`,
901.92`}, {39938.`, 908.6`}, {39939.`, 910.88`}, {39940.`,
914.65`}, {39943.`, 912.47`}, {39944.`, 922.93`}, {39945.`,
926.1`}, {39946.`, 927.3`}, {39947.`, 928.3`}, {39950.`,
920.17`}, {39951.`, 926.57`}, {39952.`, 938.68`}, {39953.`,
951.45`}, {39954.`, 957.95`}, {39957.`, 957.8`}, {39958.`,
952.9`}, {39959.`, 950.8`}, {39960.`, 959.44`}, {39961.`,
975.92`}, {39964.`, 979.62`}, {39965.`, 980.9`}, {39966.`,
963.36`}, {39967.`, 980.3`}, {39968.`, 960.82`}, {39971.`,
950.4`}, {39972.`, 953.87`}, {39973.`, 948.86`}, {39974.`,
959.3`}, {39975.`, 939.5`}, {39978.`, 927.06`}, {39979.`,
932.56`}, {39980.`, 936.`}, {39981.`, 932.58`}, {39982.`,
934.1`}, {39985.`, 921.21`}, {39986.`, 924.25`}, {39987.`,
936.29`}, {39988.`, 938.4`}, {39989.`, 940.05`}, {39992.`,
940.05`}, {39993.`, 926.68`}, {39994.`, 941.26`}, {39995.`,
931.2`}, {39996.`, 932.`}, {39999.`, 923.9`}, {40000.`,
927.65`}, {40001.`, 908.3`}, {40002.`, 915.5`}, {40003.`,
913.`}, {40006.`, 919.4`}, {40007.`, 923.93`}, {40008.`,
940.36`}, {40009.`, 935.55`}, {40010.`, 938.28`}, {40013.`,
949.32`}, {40014.`, 947.8`}, {40015.`, 952.9`}, {40016.`,
951.04`}, {40017.`, 952.25`}, {40020.`, 953.6`}, {40021.`,
937.7`}, {40022.`, 927.18`}, {40023.`, 935.22`}, {40024.`,
953.9`}, {40027.`, 956.99`}, {40028.`, 963.65`}, {40029.`,
965.92`}, {40030.`, 958.65`}, {40031.`, 954.9`}, {40034.`,
944.73`}, {40035.`, 946.11`}, {40036.`, 949.42`}, {40037.`,
955.17`}, {40038.`, 946.22`}, {40041.`, 935.78`}, {40042.`,
937.84`}, {40043.`, 944.34`}, {40044.`, 940.62`}, {40045.`,
953.08`}, {40048.`, 943.18`}, {40049.`, 943.6`}, {40050.`,
945.05`}, {40051.`, 947.39`}, {40052.`, 956.97`}, {40055.`,
951.92`}, {40056.`, 954.73`}, {40057.`, 975.82`}, {40058.`,
994.46`}, {40059.`, 991.78`}, {40062.`, 995.16`}, {40063.`,
998.32`}, {40064.`, 993.94`}, {40065.`, 996.9`}, {40066.`,
1003.9`}, {40069.`, 996.9`}, {40070.`, 1009.`}, {40071.`,
1017.2`}};
func = Fit[date, Table[t^i, {i, 0, 49}], t];
deriv2func = \!\(
\*SubscriptBox[\(\[PartialD]\), \(t, t\)]func\);
and plot:
Plot[{deriv2func}, {t, First[First[date]], First[Last[date]]},
Frame -> True, GridLines -> Automatic]
and I would like to plot additionally in this graph vertically lines, in
points which are solution of equation
deriv2fun == 0,

Maybe I need something like this
Reduce[deriv2func == 0 && 38000 < t < 41000, t, Reals], but how should I
plot this?

Beata

[dh]

Hi Beata,
you may e.g. use Reduce to get the zeros of deriv2func:

lines = t /. {Reduce[{deriv2func == 0, Element[t, Reals]}, t] //
ToRules};
lines = Line[{{ #, -0.2}, {#, 0.2}}] & /@ lines;

Plot[{deriv2func}, {t, First[First[date]], First[Last[date]]},

Frame -> True, GridLines -> Automatic, Epilog -> {Red, lines}]

Danmiel

> Reduce[deriv2func == 0&& 38000< t< 41000, t, Reals], but how should I
> plot this?
>
> Beata
>
>

--

Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:d...@metrohm.com>
Internet:<http://www.metrohm.com>

[Peter Pein]

Am 11.03.2010 12:36, schrieb Beata Warchoł:
...

> and plot:
> Plot[{deriv2func}, {t, First[First[date]], First[Last[date]]},
> Frame -> True, GridLines -> Automatic]
> and I would like to plot additionally in this graph vertically lines, in
> points which are solution of equation
> deriv2fun == 0,
>
> Maybe I need something like this

> Reduce[deriv2func == 0&& 38000< t< 41000, t, Reals], but how should I
> plot this?
>
> Beata
>

Hi Beata,

you can use Epilog inside the Plot command:

Plot[deriv2func, {t, date[[1,1]], date[[-1,1]]},
Frame->True, Axes->False, GridLines->Automatic, Epilog->Evaluate[{Green,
Line[{{t,-1},{t,1}}/.{ToRules[Reduce[
{deriv2func==0,date[[1,1]]<=t<=date[[-1,1]],Im[t]==0},t
]]}]
}]]

Peter

[Kevin J. McCann]

Try this:

tZeroDeriv = t /. Solve[deriv2func == 0, t]

(* Pick out the real values*)

zd = Extract[tZeroDeriv, Position[tZeroDeriv, _?(Im[#] == 0 &)]]

(* Now plot and use Epilog to put in the vertical lines *)

Plot[{deriv2func}, {t, First[First[date]], First[Last[date]]},

Frame -> True, GridLines -> Automatic, PlotRange -> {-0.1, 0.5},
Epilog -> {Red, (Line[{{#, -0.1}, {#, 0.5}}] &) /@ zd}]

Kevin

Beata Warcho? wrote:
> Dear Math Group,
>
> I need your help in this problem:
>
> I have date and function for example:
> date= {{39814.`, 876.34`}, {39817.`, 859.91`}, {39818.`,
> 864.55`}, {39819.`, 840.95`}, {39820.`, 853.95`}, {39821.`,

> *** snip ***

> 1017.2`}};
> func = Fit[date, Table[t^i, {i, 0, 49}], t];
> deriv2func = \!\(
> \*SubscriptBox[\(\[PartialD]\), \(t, t\)]func\);
> and plot:
> Plot[{deriv2func}, {t, First[First[date]], First[Last[date]]},
> Frame -> True, GridLines -> Automatic]

> and I would like to plot additionally in this graph vertically lines, i=

n
> points which are solution of equation
> deriv2fun == 0,
>
> Maybe I need something like this

> Reduce[deriv2func == 0 && 38000 < t < 41000, t, Reals], but how sho=
uld I
> plot this?
>
> Beata
>
>

[Bob Hanlon]

date = {{39814.`, 876.34`}, {39817.`, 859.91`},

{39818.`, 864.55`}, {39819.`, 840.95`},

{39820.`, 853.95`}, {39821.`, 856.52`},

{39943.`, 912.47`}, {39944.`, 922.93`},

Fit[date, t^Range[0, 49], t];

deriv2func = D[func, t, t];

zero = {Reduce[{
deriv2func == 0,
date[[1, 1]] <= t <= date[[-1, 1]]
}, t] // ToRules}

{{t->39895.2},{t->39966.8},{t->40023.5}}

Plot[{deriv2func}, {t, date[[1, 1]], date[[-1, 1]]},
Frame -> True,
Axes -> False,
GridLines -> Automatic,
GridLinesStyle -> GrayLevel[.8],
Epilog -> {Red,
Line[{{t, -0.11}, {t, 0.18}}] /. zero}]

Bob Hanlon

---- "Beata Warcho=C5=82" <beataw...@gmail.com> wrote:

=============
Dear Math Group,

I need your help in this problem:

I have date and function for example:
date= {{39814.`, 876.34`}, {39817.`, 859.91`}, {39818.`,
864.55`}, {39819.`, 840.95`}, {39820.`, 853.95`}, {39821.`,

1017.2`}};
func = Fit[date, Table[t^i, {i, 0, 49}], t];
deriv2func = \!\(
\*SubscriptBox[\(\[PartialD]\), \(t, t\)]func\);
and plot:
Plot[{deriv2func}, {t, First[First[date]], First[Last[date]]},
Frame -> True, GridLines -> Automatic]

and I would like to plot additionally in this graph vertically lines, in

points which are solution of equation
deriv2fun == 0,

Maybe I need something like this

Reduce[deriv2func == 0 && 38000 < t < 41000, t, Reals], but how should =
I
plot this?

Beata

--

Bob Hanlon