input bpolynomial;
input metafun
input graph
input hatching
prologues := 3;

transform T;
T := identity xscaled 10mm yscaled 1mm;

beginfig(1);
 newBPolynomial.f(2, 0, -3, -1);
 draw f.getPath(-2, 2) transformed T;
endfig;


beginfig(2);
 newBPolynomial.f(2, 0, -3, -1);
 draw f.getPath(-2, 2) transformed T;
 draw f.getTangent(-0.5)(-1, 1) transformed T;
endfig;


beginfig(3);
 dotlabeldiam := 2bp;
 labeloffset := 10bp;
 newBPolynomial.f(2, 0, -3, -1);
 draw f.getPath(-2, 2) transformed T;
 x := -0.5;
 show (x, f.eval(x));
 draw f.getTangent(x)(-1, 1) transformed T;
 dotlabel.top(btex $(-0.5, 0.25)$ etex, (x, f.eval(x)) transformed T);
endfig;

labeloffset := 3bp;

beginfig(4);
 newBPolynomial.f(2, 0, -3, -1);
 draw f'.getPath(-2, 2) transformed T;
 draw f'.getTangent(-0.25)(-1, 1) transformed T;
endfig;


beginfig(5);
 T := identity scaled 10mm;
 newBSqrRoot.s(1,0,0);
 newBCubRoot.c(1,0,0);
 draw s.getPath(0,6) transformed T;
 draw c.getPath(0,6) transformed T;
 draw s.getTangent(3)(-2, 2) transformed T;
endfig;


T := identity xscaled 10mm yscaled 1mm;
beginfig(6);
 draw getBezierFromPolynomial(2, 0, -3, -1)(-2, 2) transformed T;
endfig;


beginfig(11);
path f, g;
 xmin := -7; xmax := 7;
 ymin := -7; ymax := 7;
 %%% Define polynomials f and g.
 newBPolynomial.f(0.3, 0, -3, -1);
 f := f.getPath(xmin, xmax);
 newBPolynomial.g(0, 0.5, -2, 0);
 g := g.getPath(xmin, xmax);
 %%% Draw graph.
 draw begingraph(10cm, 6cm);
   setrange(xmin,ymin, xmax,ymax);
   autogrid(grid.bot, grid.lft) dashed evenly withcolor .9white;
   drawoptions(withpen pencircle scaled 1bp);
   gdraw f;
   gdraw g dashed evenly scaled 2;
   drawoptions();
 endgraph;
 show f;
 %%% Write table with some points of f to log file.
 show "Polynomial: " & decimal f.a & "x^3 + " &
   decimal f.b & "x^2 + " & decimal f.c & "x + " & decimal f.d;
 for x=-5 upto 5:
   show (x, f.eval(x));
 endfor
endfig;


beginfig(12);
 xmin := -6; xmax := 6;
 ymin := -6; ymax := 6;
 newBPolynomial.f(0.3, -0.5, -0.5, -1);
 draw begingraph(10cm, 6cm);
   setrange(xmin,ymin, xmax,ymax);
   autogrid(grid.bot, grid.lft) dashed evenly withcolor .9white;
   drawoptions(withpen pencircle scaled 1bp);
   %%% Draw f and its derivatives f', f'', f'''.
   gdraw f.getPath(xmin, xmax);
   gdraw f'.getPath(xmin, xmax) dashed evenly scaled 2;
   gdraw f''.getPath(xmin, xmax) dashed withdots
     withpen pencircle scaled 2bp;
   gdraw f'''.getPath(-5, 5) withcolor .6white;
   %%% Draw tangents and mark points.
   x := 2;
   drawoptions(withcolor (1, 0.6, 0.6));
   gdraw f.getTangent(x)(-2, 2);
   gdraw f'.getTangent(x)(-1, 1);
   gdraw f''.getTangent(x)(-2, 2);
   gdraw f'''.getTangent(x)(-2, 2);
   drawoptions(withcolor (0.6, 0.6, 1));
   dotlabeldiam := 2.5bp;
   gdotlabel("", (x, f.eval(x)));
   gdotlabel("", (x, f'.eval(x)));
   gdotlabel("", (x, f''.eval(x)));
   gdotlabel("", (x, f'''.eval(x)));
   drawoptions();
 endgraph;
endfig;


beginfig(13);
path f, g, A;
 xmin := -3; xmax := 6;
 ymin := -3; ymax := 6;
 newBPolynomial.f(-0.25, 0.5, 2, -1);
 newBPolynomial.g(0, 0.5, -2, 0);
 f := f.getPath(-2.5, 5.5);
 g := g.getPath(-1.5, 5.5);
 %%% Find area between f and g.
 A := buildcycle(g, reverse f);
 draw begingraph(10cm, 6cm);
   setrange(xmin,ymin, xmax,ymax);
   autogrid(grid.bot, grid.lft) dashed evenly withcolor .9white;
   %%% Fill area with transparent colour.
   gfill A withcolor transparent (1, .3, (1, 0.5, 0));
   drawoptions(withpen pencircle scaled 1bp);
   gdraw f;
   gdraw g dashed evenly scaled 2;
   drawoptions();
 endgraph;
endfig;


beginfig(14);
path f, g, A;
 T := identity xscaled 10mm yscaled 6mm;
 %%% Draw coordinate system.
 xmin := -3; xmax := 6;
 ymin := -3; ymax := 6;
 drawoptions(withpen pencircle scaled 1bp withcolor 0.8white);
 drawarrow ((xmin,0)--(xmax,0)) transformed T;
 drawarrow ((0,ymin)--(0,ymax)) transformed T;
 newBPolynomial.f(-0.25, 0.5, 2, -1);
 newBPolynomial.g(0, 0.5, -2, 0);
 f := f.getPath(-2.5, 4.2);
 g := g.getPath(-1, 5);
 A := buildcycle(g, reverse f);
 %%% Fill area with pattern.
 drawoptions();
 hatchoptions(withcolor (0.6, 0.3, 0.3));
 hatchfill A transformed T
   withcolor (-45, 2mm, -0.5bp) withcolor (45, 2mm, -0.5bp);
 drawoptions(withpen pencircle scaled 1bp);
 draw f transformed T;
 draw g transformed T dashed evenly scaled 2;
endfig;


%%%  The following figures work around a bug in metafun's
%%%  mp-form.mp package for the original figures 11 to 13.
%%%  The bug shows up when rendering negative numbers
%%%  on corrdinate axes using macro 'format'.
beginfig(21);
path f, g;
 xmin := -7; xmax := 7;
 ymin := -7; ymax := 7;
 %%% Define polynomials f and g.
 newBPolynomial.f(0.3, 0, -3, -1);
 f := f.getPath(xmin, xmax);
 newBPolynomial.g(0, 0.5, -2, 0);
 g := g.getPath(xmin, xmax);
 %%% Draw graph.
 draw begingraph(10cm, 6cm);
   setrange(xmin,ymin, xmax,ymax);
%     autogrid(grid.bot, grid.lft) dashed evenly withcolor .9white;
   for i=xmin+1 step 2 until xmax-1:
     grid.bot(decimal i, i) dashed evenly withcolor .9white;
   endfor
   for i=ymin+1 step 2 until ymax-1:
     grid.lft(decimal i, i) dashed evenly withcolor .9white;
   endfor
   drawoptions(withpen pencircle scaled 1bp);
   gdraw f;
   gdraw g dashed evenly scaled 2;
   drawoptions();
 endgraph;
 show f;
 %%% Write table with some points of f to log file.
 show "Polynomial: " & decimal f.a & "x^3 + " &
   decimal f.b & "x^2 + " & decimal f.c & "x + " & decimal f.d;
 for x=-5 upto 5:
   show (x, f.eval(x));
 endfor
endfig;


beginfig(22);
 xmin := -6; xmax := 6;
 ymin := -6; ymax := 6;
 newBPolynomial.f(0.3, -0.5, -0.5, -1);
 draw begingraph(10cm, 6cm);
   setrange(xmin,ymin, xmax,ymax);
%     autogrid(grid.bot, grid.lft) dashed evenly withcolor .9white;
   for i=xmin step 2 until xmax:
     grid.bot(decimal i, i) dashed evenly withcolor .9white;
   endfor
   for i=ymin step 2 until ymax:
     grid.lft(decimal i, i) dashed evenly withcolor .9white;
   endfor
   drawoptions(withpen pencircle scaled 1bp);
   %%% Draw f and its derivatives f', f'', f'''.
   gdraw f.getPath(xmin, xmax);
   gdraw f'.getPath(xmin, xmax) dashed evenly scaled 2;
   gdraw f''.getPath(xmin, xmax) dashed withdots
     withpen pencircle scaled 2bp;
   gdraw f'''.getPath(-5, 5) withcolor .6white;
   %%% Draw tangents and mark points.
   x := 2;
   drawoptions(withcolor (1, 0.6, 0.6));
   gdraw f.getTangent(x)(-2, 2);
   gdraw f'.getTangent(x)(-1, 1);
   gdraw f''.getTangent(x)(-2, 2);
   gdraw f'''.getTangent(x)(-2, 2);
   drawoptions(withcolor (0.6, 0.6, 1));
   dotlabeldiam := 2.5bp;
   gdotlabel("", (x, f.eval(x)));
   gdotlabel("", (x, f'.eval(x)));
   gdotlabel("", (x, f''.eval(x)));
   gdotlabel("", (x, f'''.eval(x)));
   drawoptions();
 endgraph;
endfig;


beginfig(23);
path f, g, A;
 xmin := -3; xmax := 6;
 ymin := -3; ymax := 6;
 newBPolynomial.f(-0.25, 0.5, 2, -1);
 newBPolynomial.g(0, 0.5, -2, 0);
 f := f.getPath(-2.5, 5.5);
 g := g.getPath(-1.5, 5.5);
 %%% Find area between f and g.
 A := buildcycle(g, reverse f);
 draw begingraph(10cm, 6cm);
   setrange(xmin,ymin, xmax,ymax);
%     autogrid(grid.bot, grid.lft) dashed evenly withcolor .9white;
   for i=xmin+1 step 2 until xmax:
     grid.bot(decimal i, i) dashed evenly withcolor .9white;
   endfor
   for i=ymin+1 step 2 until ymax:
     grid.lft(decimal i, i) dashed evenly withcolor .9white;
   endfor
   %%% Fill area with transparent colour.
   gfill A withcolor transparent (1, .3, (1, 0.5, 0));
   drawoptions(withpen pencircle scaled 1bp);
   gdraw f;
   gdraw g dashed evenly scaled 2;
   drawoptions();
 endgraph;
endfig;

end

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