mjhjmtu

documentclass[pstricks,border=10pt]standalone
usepackagepstricks-add,pst-plot,pst-calculate,amssymb,amsmath

begindocument
beginpspicture[algebraic](-4.5,-6)(1,2.5)
defapscalculate8/3
defbpscalculate16/3
psaxes[labels=none,Dx=2,Dy=a,xlabelPos=top,ticks=none]->(0,0)(-4.5,-6)(1,2.5)[$x$,-90][$y$,0]
psplot[plotpoints=500,linewidth=1.2pt,yMaxValue=2.1,yMinValue=-6]-53.51/3*x^3+2*x^2+4*x

uput[-45](0,0)$O$
uput[90](-2,0)$-2$
uput[90](-4,0)$-4$
uput[0](0,-a)$-dfrac83$
uput[0](0,-b)$-dfrac163$
uput[135](-2,-a)$A$
uput[180](-4,-b)$B$
psline[linestyle=dashed](0,-a)(-2,-a)(-2,0)
psline[linestyle=dashed](0,-b)(-4,-b)(-4,0)
psdots*(0,0)(-2,0)(-4,0)(0,-a)(0,-b)(-2,-a)(-4,-b)
endpspicture
enddocument

Question:

How to A-point moved from B-point to O and opposite with animation.

I have no many knowledge about animate.

works only with latex->dvips->ps2pdf

documentclassarticle
usepackagepstricks,pst-plot,pst-calculate,animate,amsmath
begindocument

%-------------------- write timeline file ---------------------%
newwriteTimeLineFile
immediateopenoutTimeLineFile=Func.txt
immediatewriteTimeLineFile::0x0,1%
multidoi=2+140immediatewriteTimeLineFile::i
immediatecloseoutTimeLineFile
%------------------- end timeline -----------------------%

pssetalgebraic

defFunc1/3*x^3+2*x^2+4*x
defbpscalculate16/3

defdrawFunc#1%
 edefYpscalculate1/3*(#1)^3+2*(#1)^2+4*(#1)
 psCoordinates[arrows=->,linecolor=blue,linestyle=dashed,
 dotstyle=o,dotscale=2,showpoints](#1,Y)
 uput[90](#1,0)$#1$
 uput[0](0,Y)Y
 uput[135](*#1 Func)$A$
 


begincenter
beginanimateinline[controls,palindrome,timeline=Func.txt,
 begin=beginpspicture(-4.5,-6)(1.1,2.75),
 end=endpspicture]10
 %---- static material: axes, labels, curve ----%
 psaxes[labels=none,xlabelPos=top,
 ticks=none]->(0,0)(-4.5,-6)(1,2.5)[$x$,-90][$y$,0]
 psplot[plotpoints=500,linewidth=1.2pt,yMaxValue=2.1,yMinValue=-6]-53.5Func
 psCoordinates[arrows=->,linestyle=dashed,dotstyle=o,dotscale=2,showpoints](*4 Func)
 uput[-45](0,0)$O$
 uput[90](-4,0)$-4$
 uput[0](0,-b)$-dfrac163$
 uput[180](-4,-b)$B$
 psCoordinates[arrows=->,linecolor=blue,linestyle=dashed,dotstyle=o,dotscale=2,showpoints](*-4 Func)
 newframe
 multiframe41rX=-4+0.1drawFuncrX%
endanimateinline% 
endcenter

enddocument

and the same as a gif animation:

Using it without a timeline:

documentclass[pstricks]article
usepackage[paperwidth=8cm,paperheight=10cm,margin=0mm]geometry
usepackagepst-plot,pst-calculate,multido,amsmath,animate
newpsstylecoorarrows=->,linecolor=blue,linestyle=dashed,dotstyle=o,dotscale=1.5,showpoints
pagestyleempty
begindocument
 pssetalgebraic

 defFunc1/3*x^3+2*x^2+4*x
 defbpscalculate16/3

defdrawFunc#1%
 beginpspicture(-4.5,-6)(1.1,2.75) 
 edefYpscalculate1/3*(#1)^3+2*(#1)^2+4*(#1)
 psCoordinates[style=coor](#1,Y)
 uput[90](#1,0)$#1$
 uput[0](0,Y)Y
 uput[135](*#1 Func)$A$
 psaxes[labels=none,xlabelPos=top,ticks=none]->(0,0)(-4.5,-6)(1,2.5)[$x$,-90][$y$,0]
 psplot[plotpoints=500,linewidth=1.2pt,yMaxValue=2.1,yMinValue=-6]-53.5Func
 psCoordinates[style=coor](*-4 Func)
 uput[-45](0,0)$O$
 uput[90](-4,0)$-4$
 uput[0](0,-b)$-dfrac163$
 uput[180](-4,-b)$B$
endpspicture%
 

beginanimateinline[poster=last, controls, palindrome]10%
 multiframe41rA=-4.0+0.1drawFuncrA%
endanimateinline

enddocument

documentclass[pstricks]standalone
usepackagepstricks-add,mathtools
deff1/3*x^3+2*x^2+4*x
psset

 unit=2cm,
 xfractionLabels,
 xfractionLabelBase=2,
 dx=pscalculate1/2,


begindocument
foreachx in14,13,...,0%
beginpspicture[algebraic](-4.6,-5.1)(1.3,2.8)
psCoordinates[linestyle=dashed](*-3.5 f)
psCoordinates[linestyle=dashed](*-xspace 4 div f)
psaxes->(0,0)(-4.4,-4.9)(1,2.5)[$x$,0][$y$,90]
psplot-3.9.5f
endpspicture
enddocument