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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 4 "Demo" }{TEXT -1 85 "\nSe
lect function\nselect point\nselect delta x\nplot fucntion and associa
ted secant line" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart;\nwith(p
lots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 196 "f := x -> x^2:  \+
# select function\na := 1:         # select point (x-coordinate)\ndx :
= 0.2:      # select Delta x\nxint := 2:        # interval for graphin
g\nyint := 2:        # interval for graphing" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 281 "b := a + dx:\nm := (f(b)-f(a))/dx:\nG1 := plot(
[f(x), f(a) + m*(x-a)], x=(a-xint)..(a+xint),\nview = [a-xint..a+xint,
f(a)-yint..f(a)+yint], color=[red,blue], scaling = constrained):\nG2 :
= plot([[a,f(a)],[b,f(b)]],style=point,symbol=circle,thickness=4,\ncol
or=black):\ndisplay(G1,G2);\nm;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 27 "#  Tangent line at a point." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 182 "f := x -> x^2;\nc := -1/2;\ng(x) := f(c) + D(f)(c)*(
x-c);\nplot([f(x),g(x)], x = c-xint..c+xint, view = [c-xint..c+xint,f(
c)-yint..f(c)+yint], color=[red,blue], scaling = constrained);\n" }}}
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