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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 28 "Curve Analysis in Calculu
s I" }}{PARA 19 "" 0 "" {TEXT -1 50 "By Sylvain Muise, smuise@student.
math.uwaterloo.ca" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 249 "This maplet
 allows Calc I students to analyze the graph of a function using first
 and second derivatives.  The student can enter a function and have th
e maplet show the intervals over which the function is increasing, dec
reasing, concave and convex." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT 256 96 "To run this maplet, click the \"Execute-Worksh
eet\"  button in the tool-bar menu (the !!! button)\n" }{TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 78 "restart: with(plots): with(plottools): with(Maplets): with(Map
lets[Elements]):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name cha
ngecoords has been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 43 "Warning
, the name arrow has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6887 "cal1Maplet := Maplet(\n  Window[W1](title=\"Calculu
s 1\", menubar=MB1, 'layout' = BL1),\n  MenuBar[MB1](Menu(\"File\", Me
nuItem(\"Close\", Shutdown()))),\n  BoxLayout[BL1](inset=0,\n    BoxCo
lumn(inset=0, spacing=0,\n      Plotter[P1]()\n    ),\n    BoxColumn(i
nset=0, spacing=0,\n      BoxRow(inset=0, spacing=0,\n        \"f(x)=
\",\n        TextField[F](\"-3*x^5+5*x^3 - 1.5*x\")\n      ),\n      B
oxRow(inset=0, spacing=0,\n        \"Domain: x= \",\n        TextField
[NEGX](3,\"-1.2\"),\n        \" to \",\n        TextField[POSX](3,\"1.
2\")\n      ),\n      Button[func](\"Show Function\", onclick=Evaluate
(P1 = 'showFunc(F, NEGX, POSX)')),\n      Button[conUp](\"Show Concave
 Up\", onclick=Evaluate(P1 = 'showConUp1(F, NEGX, POSX)')),\n      But
ton[conDown](\"Show Concave Down\", onclick=Evaluate(P1 = 'showConDown
1(F, NEGX, POSX)')),\n      Button[inc](\"Show Increasing\", onclick=E
valuate(P1 = 'showInc1(F, NEGX, POSX)')),\n      Button[dec](\"Show De
creasing\", onclick=Evaluate(P1 = 'showDec1(F, NEGX, POSX)')),\n      \+
Button[max](\"Show Max Points\", onclick=Evaluate(P1 = 'showMax1(F, NE
GX, POSX)')),\n      Button[min](\"Show Min Points\", onclick=Evaluate
(P1 = 'showMin1(F, NEGX, POSX)')),\n      Button[all](\"Show All\", on
click=Evaluate(P1 = 'showAll(F, NEGX, POSX)'))\n    )\n  )\n):\n\nshow
Func := proc(f, negX, posX) option remember:\n  plot(f,x=negX..posX, c
olor=black, thickness=3):\nend proc:\nshowConUp1 := proc(f, negX, posX
) option remember:\n  display(showConUp(f, negX, posX), showFunc(f, ne
gX, posX)):\nend proc:\nshowConDown1 := proc(f, negX, posX) option rem
ember:\n  display(showConDown(f, negX, posX), showFunc(f, negX, posX))
:\nend proc:\nshowInc1 := proc(f, negX, posX) option remember:\n  disp
lay(showInc(f, negX, posX), showFunc(f, negX, posX)):\nend proc:\nshow
Dec1 := proc(f, negX, posX) option remember:\n  display(showDec(f, neg
X, posX), showFunc(f, negX, posX)):\nend proc:\nshowMax1 := proc(f, ne
gX, posX) option remember:\n  display(showMax(f, negX, posX), showFunc
(f, negX, posX)):\nend proc:\nshowMin1 := proc(f, negX, posX) option r
emember:\n  display(showMin(f, negX, posX), showFunc(f, negX, posX)):
\nend proc:\n\nshowConUp := proc(f, negX, posX) option remember:\n  lo
cal d2, sols, i, n, polys, j, delta, X1, X2, Y1, Y2, p:\n  d2 := diff(
f,x$2);\n  sols := findRoots(d2, negX, posX);\n  if not member(evalf(n
egX), sols) then\n    sols := [evalf(negX), op(sort(sols))]:\n  end if
:\n  if not member(evalf(posX), sols) then\n    sols := [op(sort(sols)
), evalf(posX)]:\n  end if:\n  n := 100: polys := []:\n  for j from 1 \+
to (nops(sols) - 1) do\n    if evalf(subs(x = (sols[j] + sols[j+1])/2,
 d2)) > 0 then\n      delta := (sols[j+1] - sols[j]) / n:\n      X2 :=
 sols[j]:\n      for i from 1 to n do\n        X1 := evalf(X2): Y1 := \+
evalf(subs(x = X1, f)):\n        X2 := evalf(sols[j] + i * delta): Y2 \+
:= evalf(subs(x=X2,f)):\n        p[i] := polygonplot([[X1, 0],[X1, Y1]
,[X2, Y2],[X2, 0]], color=cyan, style=patchnogrid):\n      end do:\n  \+
    polys := [op(polys), seq(p[i],i=1..n)]:\n    end if:\n  end do:\n \+
 if nops(polys) = 0 then\n    return NULL:\n  end if:\n  display(seq(p
olys[i],i=1..nops(polys))):\nend proc:\n\nshowConDown := proc(f, negX,
 posX) option remember:\n  local d2, sols, i, n, polys, j, delta, X1, \+
X2, Y1, Y2, p:\n  d2 := diff(f,x$2);\n  sols := findRoots(d2, negX, po
sX);\n  if not member(evalf(negX), sols) then\n    sols := [evalf(negX
), op(sort(sols))]:\n  end if:\n  if not member(evalf(posX), sols) the
n\n    sols := [op(sort(sols)), evalf(posX)]:\n  end if:\n  n := 100: \+
polys := []:\n  for j from 1 to (nops(sols) - 1) do\n    if evalf(subs
(x = (sols[j] + sols[j+1])/2, d2)) < 0 then\n      delta := (sols[j+1]
 - sols[j]) / n:\n      X2 := sols[j]:\n      for i from 1 to n do\n  \+
      X1 := evalf(X2): Y1 := evalf(subs(x=X1,f)):\n        X2 := evalf
(sols[j] + i * delta): Y2 := evalf(subs(x=X2,f)):\n        p[i] := pol
ygonplot([[X1, 0],[X1, Y1],[X2, Y2],[X2, 0]], color=green, style=patch
nogrid):\n      end do:\n      polys := [op(polys), seq(p[i],i=1..n)]:
\n    end if:\n  end do:\n  if nops(polys) = 0 then\n    return NULL:
\n  end if:\n  display(seq(polys[i],i=1..nops(polys))):\nend proc:\n\n
showInc := proc(f, negX, posX) option remember:\n  local d1, sols, i, \+
lines, j:\n  d1 := diff(f,x);\n  sols := findRoots(d1, negX, posX);\n \+
 if not member(evalf(negX), sols) then\n    sols := [evalf(negX), op(s
ort(sols))]:\n  end if:\n  if not member(evalf(posX), sols) then\n    \+
sols := [op(sort(sols)), evalf(posX)]:\n  end if:\n  lines := []:\n  f
or j from 1 to (nops(sols) - 1) do\n    if evalf(subs(x=(sols[j]+sols[
j+1])/2,d1)) > 0 then\n      lines := [op(lines), plot(f, x=sols[j]..s
ols[j+1], color=blue, thickness=3)]:\n    end if:\n  end do:\n  if nop
s(lines) = 0 then\n    return NULL:\n  end if:\n  display(seq(lines[i]
,i=1..nops(lines))):\nend proc:\n\nshowDec := proc(f, negX, posX) opti
on remember:\n  local d1, sols, i, lines, j:\n  d1 := diff(f,x);\n  so
ls := findRoots(d1, negX, posX);\n  if not member(evalf(negX), sols) t
hen\n    sols := [evalf(negX), op(sort(sols))]:\n  end if:\n  if not m
ember(evalf(posX), sols) then\n    sols := [op(sort(sols)), evalf(posX
)]:\n  end if:\n  lines := []:\n  for j from 1 to (nops(sols) - 1) do
\n    if evalf(subs(x=(sols[j] + sols[j+1])/2,d1)) < 0 then\n      lin
es := [op(lines), plot(f, x=sols[j]..sols[j+1], color=orange, thicknes
s=3)]:\n    end if:\n  end do:\n  if nops(lines) = 0 then\n    return \+
NULL:\n  end if:\n  display(seq(lines[i],i=1..nops(lines))):\nend proc
:\n\nshowMax := proc(f, negX, posX) option remember:\n  local d1, d2, \+
sols, i, p:\n  d1 := diff(f,x);\n  d2 := diff(f,x$2);\n  sols := findR
oots(d1, negX, posX);\n  p := []:\n  for i from 1 to nops(sols) do\n  \+
  if evalf(subs(x=sols[i],d2)) < 0 then\n      p := [op(p), line([sols
[i],0],[sols[i],subs(x=sols[i], f)],color=blue,thickness=3)]:\n    end
 if:\n  end do:\n  if nops(p) = 0 then\n    return NULL:\n  end if:\n \+
 display(seq(p[i],i=1..nops(p))):\nend proc:\n\nshowMin := proc(f, neg
X, posX) option remember:\n  local d1, d2, sols, i, p:\n  d1 := diff(f
,x);\n  d2 := diff(f,x$2);\n  sols := findRoots(d1, negX, posX);\n  p \+
:= []:\n  for i from 1 to nops(sols) do\n    if evalf(subs(x=sols[i],d
2)) > 0 then\n      p := [op(p), line([sols[i],0],[sols[i],subs(x=sols
[i], f)],color=red,thickness=3)]:\n    end if:\n  end do:\n  if nops(p
) = 0 then\n    return NULL:\n  end if:\n  display(seq(p[i],i=1..nops(
p))):\nend proc:\n\nshowAll := proc(f, negX, posX) option remember:\n \+
 display(showMin(f, negX, posX), showMax(f, negX, posX), showConDown(f
, negX, posX), showConUp(f, negX, posX), showDec(f, negX, posX), showI
nc(f, negX, posX)):\nend proc:\n\nfindRoots := proc(f, negX, posX) opt
ion remember:\n  local n, i, delta, li, X1, X2, sol, IN, j:\n  n := 10
0:\n  li := []:\n  delta := (evalf(posX) - evalf(negX)) / n:\n  X2 := \+
evalf(negX):\n  for i from 1 to n do\n    X1 := evalf(X2): X2 := evalf
(negX + i * delta):\n    sol := fsolve(f = 0, x = X1 .. X2):\n    if t
ype(sol, numeric) then\n      if not member(sol, li) then\n        li \+
:= [ op(li), evalf(sol)]:\n      end if:\n    end if:\n  end do:\n  li
;\nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Display(cal
1Maplet);" }}{PARA 6 "" 1 "" {TEXT -1 38 "Initializing Java runtime en
vironment." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 78 }{VIEWOPTS 1 
1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }