(*^
::[ Information =
"This is a Mathematica Notebook file. It contains ASCII text, and can be
transferred by email, ftp, or other text-file transfer utility. It should
be read or edited using a copy of Mathematica or MathReader. If you
received this as email, use your mail application or copy/paste to save
everything from the line containing (*^ down to the line containing ^*)
into a plain text file. On some systems you may have to give the file a
name ending with ".ma" to allow Mathematica to recognize it as a Notebook.
The line below identifies what version of Mathematica created this file,
but it can be opened using any other version as well.";
FrontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.2";
MacintoshStandardFontEncoding;
fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8, 24, "Times";
fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6, 18, "Times";
fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6, 14, "Times";
fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20, 18, "Times";
fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15, 14, "Times";
fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12, 12, "Times";
fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times";
fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5, 12, "Courier";
fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier";
fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5, 12, "Courier";
fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier";
fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5, 12, "Courier";
fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, 12, "Courier";
fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, 10, "Geneva";
fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = leftheader, inactive, L2, 12, "Times";
fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7, 12, "Times";
fontset = leftfooter, inactive, L2, 12, "Times";
fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times";
fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
paletteColors = 128; automaticGrouping; currentKernel;
]
:[font = input; preserveAspect]
ClearAll;
$DefaultFont = {"Times-Roman",10};
Needs["Graphics`Graphics`"];
a = 40.7; b = 43.6;
maize = {{12,0}, {15,9}, {20,20}, {25,29},
{30,35}, {35,38}, {45,30}, {50,7}, {51,0}};
m0[t_]:= t(t-12)(51-t)(1884 - 71 t + t^2);
approxm[t_] = Fit[maize,{m0[t]},t];
s = Abs[FindMinimum[-approxm[t],{t,37,37.1}][[1]]];
appm[t_] = approxm[t]/s;
tang = D[appm[t],t]/.t->a;
chor = (appm[b] - appm[a])/(b-a);
xl = a - appm[a]/tang;
xh = a + (1.05 - appm[a])/tang;
xl2 = a - appm[a]/chor;
xh2 = a + (1.05 - appm[a])/chor;
line0 = Graphics[{Dashing[{0.001,0.01}],
Line[{{xl,0},{xh,1.05}}]}];
line1 = Graphics[{Dashing[{0.01,0.01}],
Line[{{xl2,0},{xh2,1.05}}]}];
line2 = Graphics[{Thickness[0.0008],
Line[{{a,appm[a]},{a,appm[b]}}]}];
line3 = Graphics[{Thickness[0.0008],
Line[{{a,appm[b]},{b,appm[b]}}]}];
circ1 = Graphics[Disk[{a,appm[a]},{0.7,0.015}],
AspectRatio->Automatic];
circ2 = Graphics[Disk[{b,appm[b]},{0.7,0.015}],
AspectRatio->Automatic];
text = Graphics[{Text[FontForm["x + x",{"Times-Roman",10}],{b+0.5,-0.035}],
Text[FontForm[d,{"Symbol",9}],{b + 1.4,-0.031}],
Text[FontForm["y + y",{"Times-Roman",10}],{-2.5,appm[b]}],
Text[FontForm[d,{"Symbol",9}],{-1.5,appm[b]+0.005}],
Text[FontForm[d,{"Symbol",9}],{a-2.35,appm[b]+0.005}],
Text[FontForm["(x,y + y)",{"Times-Roman",10}],{a-4,appm[b]}]}];
plot = Plot[appm[t],{t,12,51},
PlotLabel -> "Figure 16.2\n\n y = F(x)",
Ticks->{{12,{a," "},{b," "}},
{{appm[a],"y"},{appm[b]," "}}},
PlotRange->{{-5,90},{-0.1,1.05}}];
Show[plot, line0, line1, line2, line3, circ1, circ2,text]
^*)