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Cubic Equation Demonstration

Posted 10 years ago
Dear,

 I saw the CDF example "Cubic Equation" at the Wolfram site http://demonstrations.wolfram.com/CubicEquation/. The author made available the Mathematica code in order the reader could learn a high level development. So I typed all the code (you can not copy because the code is in a .png file) and run to verify my typing. I verify many times but the code did not work well (it did not plot the zeros, inflection points and critical points). Bellow you can see the code and I ask you to help me to understand what happend.
 Manipulate[
 
 Plot[a3 x^3 + a2 x^2 + a1 x + a0, {x, -2, 2}, PlotRange -> 10,
   PlotLabel -> TraditionalForm[a3 x^3 + a2 x^2 + a1 x + a0],
   PlotStyle -> Thickness[.005],
   Epilog -> {
     PointSize[.015],
     (*KEY*)
     {RGBColor[1, .26, .0], Point[{1.2, 7}]},
    Text[Style["zeros", 12, Italic], {1.3, 7}, {-1, 0}],
    {RGBColor[.12, .61, .78], Point[{1.2, 6}]},
    Text[Style["critical points", 12, Italic], {1.3, 6}, {-1, 0}],
    {RGBColor[.67, .75, .15], Point[{1.2, 5}]},
    Text[Style["inflection points", 12, Italic], {1.3, 5}, {-1, 0}],
    (*zeros*)
    RGBColor[1, .26, .0],
    If[Flatten[#] === {}, {},
       Point[{#, Function[x, a3 x^3 + a2 x^2 + a1  x + a0][#]}] & /@
                                    {x /. #}] &[{ToRules[
       Quiet@Reduce[a3 x^3 + a2 x^2 + a1 x + a0 == 0, x, Reals]]}],
    (*critical points*)
    RGBColor[.12, .61, .78],
    If[Flatten[#] === {}, {},
       Point[{#, Function[x, a3 x^3 + a2 x^2 + a1 x + a0][#]}] & /@
                                    {x /. #}] &[{ToRules[
       Quiet@Reduce[3 x^2 a3 + 2 a2 x + a2 x^2 + a1 == 0, x, Reals]]}],
    (*inflection points*)
    RGBColor[.67, .75, .15],
    If[Flatten[#] === {}, {},
       Point[{#, Function[x, a3 x^3 + a2 x^2 + a1 x + a0][#]}] & /@
                                    {x /. #}] &[{ToRules[
       Quiet@Reduce[6 x a3 + 2 a2 x + 2 a2 == 0, x, Reals]]}]
    }, ImageSize -> {500, 400}], {a3, -5, 5}, {a2, -5, 5}, {a1, -5,
  5}, {a0, -5, 5}]
Thank you,
Ana
POSTED BY: Ana Squadri
3 Replies
It is a typo, the original code has in several places
(x /. #)
while you have
{x /. #}
Also your second derivative isn't quite right, should be just 6 x a3 + 2 a2.

There is a link to download a notebook, where it says 'Download Author Code' (not 'preview'), so it shouldn't be necessary to copy the code from the picture.
POSTED BY: Ilian Gachevski
Posted 10 years ago
It is not mine. I just copy. I open the .nb file. His preview is totally wrong. Thank you
POSTED BY: Ana Squadri
The preview seems completely fine to me. Besides, I think the image is automatically generated from the notebook, so there isn't too much room for errors.
POSTED BY: Ilian Gachevski
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