Graphs of derivatives

This Mathematica notebook is licensed under a MouseOver .

The  notebook contains the code used to create the MouseOver on abstractmath.org.
It is raw code and contains a few errors.  Some of the graphs differ from the graphs on the website.  I have no present intention to turn this into an easy-to-use package, but everyone should feel free to use and and adapt it under the CC Share-Alike license.

The notebook takes several minutes to evaluate.

GT := 2

f[x_] := -.5 + .5x +.2 x^2 -.21 x^3 -.015x^4 + .01 x^5

Plot[{f[x],f'[x],f''[x],f'''[x],f''''[x]}, {x,-4,4}, PlotRange->{-4,4}, AspectRatio->1,  ImageSize -> {400,400}, Prolog -> AbsoluteThickness[GT],
PlotStyle->{{RGBColor[0,0,1]},{RGBColor[1,0,0]},{RGBColor[0,1,0]}, RGBColor[.7,.7,0],RGBColor[0.7,0,.7]}]

SD[f_,n_,a_,b_, c_, d_, s_] := ((r := (d-c)/(b-a)); Plot[Take[{f[x],f'[x],f''[x],f'''[x],f''''[x]}, n] // Evaluate,{x,a,b}, PlotRange->{c,d},Prolog->AbsoluteThickness[GT], AspectRatio->r, ImageSize -> { s,r s},PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[1,0,0]},{RGBColor[0,1,0]}, RGBColor[.7,.7,0],RGBColor[.7,0,.7]}])

SD[f,5,-5,5,-4,4,400]

f[x_]:=-.5+.5x+.2 x^2-.19 x^3-.015x^4+.01 x^5

SD[f,5,-5,5,-5,5,500]

f[x_] := -.5 + .5x +.2 x^2 -.2 x^3 -.015x^4 + .01 x^5

Plot[{f[x],f'[x],f''[x],f'''[x],f''''[x]}, {x,-4,7}, PlotRange->{-4,4}, Prolog -> AbsoluteThickness[GT], AspectRatio->1, ImageSize -> {400,400}, PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[1,0,0]},{RGBColor[0,1,0]}, RGBColor[.7,.7,0],RGBColor[0,.7,.6]}]

{f[x], f'[x]}

Plot[{f[x],f'[x]}, {x,-4,4}, PlotRange->{-4,4},ImageSize->{400,400},  AspectRatio->1, Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[1,0,0]},{RGBColor[0,1,0]}, RGBColor[.7,.7,0],RGBColor[0,.7,.6]}]

Take[{a,b,c,d},2]

L := {a,b,c,d,e}

Take[L,3]

Table[i,{i,5}]

Take[{f[x],f'[x], f''[x]},2]

f[x_] := x^2/4 // N;
Plot[Take[{f[x],f'[x], f''[x]},2] // Evaluate, {x,-4,4}, PlotRange->{-4,4}, AspectRatio->1, ImageSize->{400,400}, Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[1,0,0]},{RGBColor[0,1,0]}, RGBColor[.7,.7,0],RGBColor[0,.7,.6]}]

{f[x], f'[x], f''[x]}

ShowDerivatives[f_,n_,a_,b_] :=Plot[Take[{f[x],f'[x],f''[x],f'''[x],f''''[x]}, n] // Evaluate,{x,a,b}, Prolog->AbsoluteThickness[GT],PlotRange->{a,b}, AspectRatio->1, ImageSize -> {400,400},PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[1,0,0]},{RGBColor[0,1,0]}, RGBColor[.7,.7,0],RGBColor[.7,0,.7]}]

ShowDerivatives[f,3,-2,2]

Remove[f]

DF[f_,n_]:=Take[{{"f",f[x]},{"f'",f'[x]},{"f''",f''[x]},{"f'''",f'''[x]},{"f''''",f''''[x]}}, n] // TableForm // TraditionalForm

f[x_] := Sin[(x^2)-1]

DF[f,5]

f'[x]

ShowDerivatives[f,2,-12,12]

f[x_] := 2+(1/30)(x-3)^2+Sin[ x]

f'[x]

f''[x]

ShowDerivatives[f,3,-15,15]

ShowDerivatives[f,4,-6,6]

ShowDerivatives[f,3,-11,11]

ShowDerivatives[f,5,-11,11]

Remove[f]

f[x_] := Sin[x]

Sin[x+(Pi/2)]

Plot[{Sin[x], Cos[x]},{x, -2 Pi, 2 Pi}, PlotRange -> {-1.5,1.5}, Prolog->AbsoluteThickness[GT],ImageSize -> {3  170, 170}, AspectRatio->3/(4 Pi), PlotStyle->{{RGBColor[0,0,1]},RGBColor[1,0,0]}]

Plot[{Sin[x], Cos[x], -Sin[x], -Cos[x]},{x, -2 Pi, 2 Pi}, PlotRange -> {-1.5,1.5}, ImageSize -> {((4 Pi)/3 )200, 200}, AspectRatio->3/(4 Pi), Prolog->AbsoluteThickness[GT],PlotStyle->{RGBColor[0,0,1],RGBColor[1,0,0],RGBColor[0,1,0], RGBColor[.7,.7,0]}]

Remove[f]

f[x_] := Sin[x]

SD[f,4,-2 Pi, 2 Pi, -1.5, 1.5, 700]

Remove[f]

Plot[{x^2, 2 x},{x, -2 , 2 }, PlotRange -> {-4,4}, ImageSize -> {300,300}, Prolog->AbsoluteThickness[GT],AspectRatio->2, PlotStyle->{{RGBColor[0,0,1]},RGBColor[1,0,0]}]

Remove[f]

f[x_] := Tan[x/2]

f'[x]

f''[x]

f'''[x]

(1/4) ((Sec[(x/2)])^4)+(1/2) ((Sec[(x/2)])^2) ((Tan[(x/2)])^2)

f''''[x]

ShowDerivatives[f,5,-Pi,Pi]

f[x_] := Tan[x]

ShowDerivatives[f,5,-Pi,Pi]

Remove[f]

f[x_] := (10/(x+1))  Sin[x]

f'[x]

f''[x]

ShowDerivatives[f,5,-2 Pi,2 Pi]

Plot[{f[x],f'[x],f''[x],f'''[x],f''''[x]},{x,-.99,7},PlotRange->{-6,6},AspectRatio->3/2,ImageSize->{400,3/2 400},Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]},{RGBColor[1,0,0]},{RGBColor[0,1,0]},RGBColor[.7,.7,0],RGBColor[0.7,0,.7]}]

Plot[{f[x],f'[x],f''[x],f'''[x],f''''[x]},{x,-.99,19},Prolog->AbsoluteThickness[GT],PlotRange->{-10,10},AspectRatio->1,ImageSize->{500,500},PlotStyle->{{RGBColor[0,0,1]},{RGBColor[1,0,0]},{RGBColor[0,1,0]},RGBColor[.7,.7,0],RGBColor[0.7,0,.7]}]

f''''[x]

Plot[{f[x],f'[x],f''[x],f'''[x],f''''[x]},{x,-.99,59},Prolog->AbsoluteThickness[GT],PlotRange->{-30,30},AspectRatio->1,ImageSize->{1200,1200},PlotStyle->{{RGBColor[0,0,1]},{RGBColor[1,0,0]},{RGBColor[0,1,0]},RGBColor[.7,.7,0],RGBColor[0.7,0,.7]}]

f[300] - f''''[300] // N

ShowDerivatives[f,3,-1.0000000001 ,-0.999999999 ]

Remove[f]

f[x_] := 0 /; x  <= -0.99 && x >= -1.01;
f[x_] := (10/(x+1))  Sin[x] /; x  < -1.01;
f[x_] := (10/(x+1))  Sin[x] /; x  > -0.99;

ShowDerivatives[f,3,-2 Pi,2 Pi]

f[x_] := ArcTan[x]

f'[x]

f''[x]

f'''[x]

ShowDerivatives[f,5,-Pi,Pi]

ShowDerivatives[f,4,-Pi,Pi]

SD[f,4,-4,4,-2.5,1.4,500]

f[x_] := Exp[-x^2]

ShowDerivatives[f,4,-4,4]

Remove[f]

f[x_] := (1/Sqrt[2 Pi])Exp[-(x^2)/2]

SD[f,4,-3,3,-1,1,600]

6

f[x_] := Pochhammer[x,4]

ShowDerivatives[f,2,-4,3]

f[x_] := BetaRegularized[x,2,2]

ShowDerivatives[f,2,-1,2]

f[x_] := BetaRegularized[x,.5,2]

ShowDerivatives[f,3,-1,3]

f[x_] := Beta[x,1,.5,2]

f[x]

ShowDerivatives[f,5,-2,4]

f[x_] := LogGamma[x]

ShowDerivatives[f,3,-10, 10]

f[x_] := Erf[x]

ShowDerivatives[f,4,-3, 3]

f[x_] := Sin[x^2-1]

ShowDerivatives[f,2,-2, 2]

g[x_] := 2 x

Plot[{f[x],f'[x], g[x]},{x, -3, 3}, PlotRange -> {-6,6}, ImageSize -> {200,2 200}, AspectRatio->2, Prolog->AbsoluteThickness[GT],PlotStyle->{RGBColor[0,0,1],RGBColor[1,0,0],RGBColor[0,0,0]}]

Plot[{f[x],f'[x], g[x]},{x, -4,4}, PlotRange -> {-8,8}, ImageSize -> {300,2 300}, AspectRatio->2, Prolog->AbsoluteThickness[GT],PlotStyle->{RGBColor[0,0,1],RGBColor[1,0,0],RGBColor[0,0,0]}]

Plot[{f[x],f'[x]},{x, -4, 4}, PlotRange -> {-9,9}, ImageSize -> {200,2 200}, AspectRatio->2.25, Prolog->AbsoluteThickness[GT],PlotStyle->{RGBColor[0,0,1],RGBColor[1,0,0],RGBColor[0,1,0]}]

g[x_] := Integrate[f[x],x]

g[x]

g[1]

C[x]

S[x]

g[x] // FullSimplify

g[2]

S[Sqrt[(2/Pi)  x]]

S[Sqrt[(2/Pi)  2]]

ShowDerivatives[g,2,-5, 5]

ShowDerivatives[g,3,-5, 5]

h[t_] := Integrate[f[x],{x,0,t}]

h[t]

h[3]

% // N

h[t] // N

g[x_] := Exp[.8  x]

ShowDerivatives[g,5,-1, 3]

Integrate[Sin[t^2], {t,0,x}]

g[x_] := Integrate[Sin[t^2], {t,0,x}]
h[x_] := Sin[x^2]

ShowDerivatives[g,2,-6,6]

Integrate[Exp[t^2], {t,0,x}]

g[x_] := Integrate[Exp[t^2], {t,0,x}]
h[x_] := Exp[x^2]

ShowDerivatives[g,3,-3,3]

Remove[f]

f[x_] := Sqrt[(1-x)^2]

ShowDerivatives[f,3,-3,3]

Remove[f]

f[x_] := Log[x+1]

DF[f,5]

ShowDerivatives[f,5,-1,3]

f[x_] := Log[x]

DF[f,5]

GT := 2

SD[f,5,0.01,11,-4,4,350]

Remove[f]

f[x_] := Log[10,x]

SD[f,5,0.01,11,-4,4,400]

Remove[f]

f[x_] := x Log[x]

DF[f,5]

SD[f,5,0.01,5,-4,4,300]

Remove[f]

f[x_]:=Log[x]/x

DF[f,5]

SD[f,5,0.01,4,-3,4,300]

Remove[f]

f[x_] := ArcSin[x]

DF[f,5]

SD[f,4,-1,1,-2,3,200]

Remove[f]

f[x_]:=ArcSec[x]

DF[f,5]

SD[f,5,1,5,-3,3,300]

Remove[f]

f[x_] := x Sin[x]

ShowDerivatives[f,5,-7,7]

f[x_] := x Exp[x] - x^2

ShowDerivatives[f,5,-4,4]

f[x_] := Sin[x] Cos[x]

DF[f,3] //TraditionalForm

ShowDerivatives[f,3,-4,4]

SD[f,4,-4,4,-4,4,400]

f[x_] := Exp[x] Sin[x]/2

ShowDerivatives[f,3,-4,4]

f[x_] := Sin[Exp[x]]

ShowDerivatives[f,2,-4,4]

f[x_] := 3 Sin[Sin[x]]

ShowDerivatives[f,3,-10,10]

f[x_] := Exp[Sin[x]]

ShowDerivatives[f,4,-12,12]

f[x_] := Sin[(x^2)/3]

ShowDerivatives[f,2,-10,10]

f[x_] := Exp[-x/2]  Sin[Sqrt[3] x / 2]
ShowDerivatives[f,3,-4,4]

f[x_] :=1/2  Exp[-x/2]  Sin[Sqrt[3] x / 2]

{f[x], f'[x], f''[x]}

ShowDerivatives[f,3,-6,6]

f[x_] :=1/5  Exp[-x/2]  Sin[Sqrt[3] x / 2]

{f[x], f'[x], f''[x], f'''[x]}

Plot[{f[x],f'[x], f''[x]}, {x,-8,2}, PlotRange->{-7,7}, AspectRatio->7/5, Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[1,0,0]},{RGBColor[0,1,0]}, RGBColor[.7,.7,0],RGBColor[0,.7,.6]}, ImageSize -> {300,600}]

f[x_] :=1/5  Exp[x/2]  Cos[Sqrt[3](- x )/ 2]

{f[x], f'[x], f''[x], f'''[x]}

Plot[{f[x],f'[x], f''[x], f'''[x]}, {x,-2,8}, PlotRange->{-7,7}, AspectRatio->7/5, Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[1,0,0]},{RGBColor[0,1,0]}, RGBColor[.7,.7,0],RGBColor[0,.7,.6]}, ImageSize -> {300,600}]

f[x_] :=1/5  Exp[x/2]  Sin[Sqrt[3](-x )/ 2]

{f[x], f'[x], f''[x], f'''[x]}

f[x_] :=1/5  Exp[x/2]  Sin[Sqrt[3](x )/ 2]

{f[x], f'[x], f''[x], f'''[x]}

f[x_] :=1/5  Exp[-x/2]  Sin[Sqrt[3](x )/ 2]

{f[x], f'[x], f''[x], f'''[x]}

f[x_] :=-1/5  Exp[x/2]  Sin[Sqrt[3](-x )/ 2]

{f[x], f'[x], f''[x], f'''[x]}

ShowDerivatives[f,4,-6,6]

f[x_] :=1/5  Exp[-x/2]  Sin[Sqrt[3](x )/ 2]

ShowDerivatives[f,4,-6,6]

ShowDerivatives[f,3,-6,6]

f[x_] :=1/5  Exp[-x/2]  Sin[Sqrt[3](x )/ 2]Exp[x]

ShowDerivatives[f,4,-6,6]

f[x_] :=1/5  Exp[-x/2]  Sin[Sqrt[3](x )/ 2]+ Exp[x]

ShowDerivatives[f,3,-6,6]

f[x_] :=1/5  Exp[x/2]  Cos[Sqrt[3](- x )/ 2]

ShowDerivatives[f,4,-6,6]

f[x_] :=1/2  Exp[-x/2]  Sin[a x]

{f[x], f'[x], f''[x], f'''[x]}

f[x_] := Exp[-x/2]  Sin[1.1 Sqrt[3] x / 2]

DF[f,5]

ShowDerivatives[f,4,-6,6]

SD[f,5,-6,6,-10,6,400]

Plot[{f[x],f'[x], f''[x], f'''[x]}, {x,-6,6}, PlotRange->{-9,9}, AspectRatio->3/2, Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[1,0,0]},{RGBColor[0,1,0]}, RGBColor[.7,.7,0],RGBColor[0,.7,.6]}, ImageSize -> {600,400}]

f[x_] := Exp[-x/2]  Sin[ x / 2]

DF[f,5]

SD[f,5,-8,6,-10,5,400]

Remove[f]

f[x_] := Sin[x]

ShowDerivatives[f,4,-6,6]

Plot[{f[x],f'[x], f''[x], f'''[x]}, {x,-6,6}, PlotRange->{-2,2}, AspectRatio->1/3, Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[1,0,0]},{RGBColor[0,1,0]}, RGBColor[.7,.7,0],RGBColor[0,.7,.6]}, ImageSize -> {600,200}]

f[x_] := Sin[1.1 x]

ShowDerivatives[f,5,-6,6]

Plot[{f[x],f'[x], f''[x], f'''[x], f''''[x]}, {x,-6,6}, PlotRange->{-2,2}, AspectRatio->1/3, Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[1,0,0]},{RGBColor[0,1,0]}, RGBColor[.7,.7,0],RGBColor[0,.7,.6]}, ImageSize -> {600,200}]

f[x_] := Exp[-x]

ShowDerivatives[f,2,-2,2]

Plot[{f[x],f'[x]}, {x,-2,2}, PlotRange->{-4,4}, AspectRatio->2, Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[1,0,0]},{RGBColor[0,1,0]}, RGBColor[.7,.7,0],RGBColor[0,.7,.6]}, ImageSize -> {400,400}]

f[x_] := 1

ShowDerivatives[f,2,-2,2]

f[x_] := x

ShowDerivatives[f,3,-2,2]

f[x_] := 1/2 x

ShowDerivatives[f,3,-2,2]

f[x_] := x^2

ShowDerivatives[f,4,-3,3]

g[x_] := x-(1/4)

h[x_] := -2 x - 1

Plot[{f[x],f'[x],f''[x],h[x],g[x]},{x,-4,4},PlotRange->{-4,4},AspectRatio->1,ImageSize->{400,400},Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]},{RGBColor[1,0,0]},{RGBColor[0,1,0]},RGBColor[0,0,0],RGBColor[0,0,0]}]

Remove[f,g, h]

f[x_] := Exp[x]; g[x_] := x+1;  h[x_] := E x

Plot[{f[x], g[x], h[x]}, {x,-2,2}, PlotRange->{-1,5}, AspectRatio->3/2, Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[0,0,0]},{RGBColor[0,0,0]}, RGBColor[.7,.7,0],RGBColor[0,.7,.6]}, ImageSize -> {300,450}]

f[x_] = Exp[0.8 x]

Plot[{f[x],f'[x], f''[x], f'''[x], f''''[x]}, {x,-2,2}, PlotRange->{-1,5}, AspectRatio->3/2, Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[1,0,0]},{RGBColor[0,1,0]}, RGBColor[.7,.7,0],RGBColor[0,.7,.6]}, ImageSize -> {300,450}]

Remove[f]

f[x_] := Exp[1.1 x]

Plot[{f[x],f'[x], f''[x], f'''[x], f''''[x]}, {x,-2,2}, PlotRange->{-1,5}, AspectRatio->3/2, Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[1,0,0]},{RGBColor[0,1,0]}, RGBColor[.7,.7,0],RGBColor[0,.7,.6]}, ImageSize -> {300,450}]

f[x_] := Exp[0.9 x]

Plot[{f[x],f'[x], f''[x], f'''[x], f''''[x]}, {x,-2,2}, PlotRange->{-1,5}, AspectRatio->3/2, Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[1,0,0]},{RGBColor[0,.9,0]}, RGBColor[.7,.7,0],RGBColor[.7,0,.7]}, ImageSize -> {300,450}]

f[x_] := .05 Log[x] Exp[x]

Plot[{f[x],f'[x], f''[x], f'''[x], f''''[x]}, {x,.01,3}, PlotRange->{-1,5}, AspectRatio->3/2, Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]}, {RGBColor[1,0,0]},{RGBColor[0,1,0]}, RGBColor[.7,.7,0],RGBColor[0=.7,0,.7]}, ImageSize -> {300,450}]

SD[f,5,0.01,3,-1,2,300]

f[x_] := Exp[ArcTan[x]]

ShowDerivatives[f,4,-4,4]

f[x_] := ArcTan[Exp[x]]

ShowDerivatives[f,4,-3,3]

f[x_] :=.4  Tan[Sin[x]]

ShowDerivatives[f,4,-3,3]

f[x_] := Sin[Tan[x/3]]

ShowDerivatives[f,4,-Pi,Pi]

ShowDerivatives[f,4,-4.2,4.2]

f[x_] := Sec[x]

f'[x]

f''[x]

f'''[x]

SD[f,3,-1.2,1.2,-2,4,200]

Remove[f,g,h]

f[x_]:=Abs[x]

DF[f,2]

ShowDerivatives[f,2,-3,3]

g[x_] := 1 /; x > 0

h[x_] := -1 /; x < 0

Plot[{f[x],g[x], h[x]},{x,-3,3},PlotRange->{-3,3},AspectRatio->1,ImageSize->{400,400},Prolog->AbsoluteThickness[GT],PlotStyle->{{RGBColor[0,0,1]},{RGBColor[1,0,0]},{RGBColor[1,0,0]},RGBColor[.7,.7,0],RGBColor[0.7,0,.7]}]

Remove[a]

a[n_] :=1/(n!) /; Mod[n,3] ==1 ; 
a[n_] :=-1/((n+1)!) /; Mod[n,3] == 2; 
a[n_] := 0

Remove[f]

f[x_] := Sum [a[i] x^i, {i, M}]

M:=50

SD[f, 3,-7,4,-10,10,200]

a[n_] :=1/(n!) /; Mod[n,3] ==3 ; 
a[n_] :=-1/((n^n)) /; Mod[n,3] == 2; 
a[n_] := 0

Remove[f,g,h]

f[x_] := x^3

DF[f,5]

SD[f,3,-1.4,1.4,-2,2,300]

SD[f,4,-1.6,1.6,-1.5,6.5,300]

f[x_] := (x^3)-x

SD[f,3,-1.4,1.4,-2,1.5,300]

f[x_] :=0.25 (x^4)

DF[f,5]

SD[f,4,-1.4,1.4,-1.5,1.5,300]

Remove[f]

f[x_] := 0.25 ((x^4)-(x^2)+x)

f[x]

DF[f,5]

SD[f,4,-2,2,-2,3,300]

f[x_] := 0.25 ((x^4)-(x^3)-x)

SD[f,4,-2,2,-2,3,300]

f[x_] := 0.25 ((x^4)-(x^3)+ (x^2)-x)

SD[f,4,-2,2,-2,3,300]

f[x_] := 0.25 (x (x+1) (x-1) (x-1.5))

SD[f,4,-2,2,-2,3,300]

DSolve[y'''[x] == y[x], y, x]

f[x_] := Exp[-x/2] Sin[(Sqrt[3]/2) x]

SD[f,3,-4,4,-4,3,300]

f[x_] := (x^2-1)/(x^2+1)

DF[f,5]

SD[f,3,-3,3,-2,4.2,400]

f[x_] := (x^4)/((x^2+1)(x^2+2))

SD[f,3,-3,3,-1,1,500]

f[x_] := 1/(x^2)

DF[f,5]

SD[f,5,0.01,4,-3,3,200]

DSolve[y''[x] == y[x]y'[x],y,x]

DSolve[y''[x]-y'[x] == y[x],y,x]

Exp[1] // N

Plot[{x^2, (x^2)-1,  (x^2)+1,(x^2)+1.3,(x^2)+1.2,  (x^2)+Pi/2},{x, -2 , 2 }, PlotRange -> {-2,4}, ImageSize -> {500,500}, Prolog->AbsoluteThickness[GT],AspectRatio->3/2, PlotStyle->{{RGBColor[0,0,1]}}]