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{SECT 0 {SECT 0 {PARA 3 "" 0 "" {TEXT -1 20 "Derivative animation" }}

{PARA 0 "" 0 "" {TEXT -1 63 "This is a general-purpose worksheet for a

nimating a derivative." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 20 "Specif

ic definitions" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f:=x->1+x^

2; " }{TEXT -1 27 "The function to be graphed." }}{PARA 11 "" 1 "" 

{XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&arrowGF(,&\"\"\"F-*$)9$

\"\"#F-F-F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "a:=2:   \+

   " }{TEXT -1 57 "x value at which to draw the tangent line and put s

ecants" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "xmax:=a+4: " }

{TEXT -1 27 "Maximum x value in the plot" }}}{EXCHG {PARA 0 "> " 0 "" 

{MPLTEXT 1 0 11 "xmin:=a-4: " }{TEXT -1 27 "Minimum x value in the plo

t" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "hmax:=3:   " }{TEXT 

-1 24 "How far to the right of " }{TEXT 256 1 "a" }{TEXT -1 29 " to go

 with the secant points" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "

ysize:=1.5:  " }{TEXT -1 58 "The height of the vertical line at the se

cond secant point" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 17 "General pr

ocedure" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(plots): " }

{TEXT -1 13 "Includes the " }{TEXT 258 7 "display" }{TEXT -1 22 " func

tion needed below" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name ch

angecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 

1 0 36 "p1:=plot(f,xmin..xmax,color=black): " }{TEXT -1 24 "Plot the f

unction itself" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "p2:=plot(

[a,f(a)-x,x=-ysize..ysize],numpoints=2,color=violet): " }{TEXT -1 19 "

A vertical line at " }{TEXT 257 8 "(a,f(a))" }{TEXT -1 0 "" }}}{EXCHG 

{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "p3:=plot(f(a)+D(f)(a)*(x-a),x=xmin.

.xmax,numpoints=2,color=blue): " }{TEXT -1 16 "The tangent line" }}}

{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "p4:=animate(f(a)+((f(-t)-f(

a))/(-t-a))*(x-a), x=xmin..xmax, t=-a-hmax..-a,frames=100,numpoints=2,

color=red): " }{TEXT -1 49 "Animated secant lines from the right.  Not

e that " }{TEXT 259 1 "t" }{TEXT -1 64 " is deliberately the negative \+

of what it should be, so that the " }{TEXT 260 1 "t" }{TEXT -1 31 " ra

nge goes from left to right." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 

0 104 "p5:=animate([-t,f(-t)+x,x=-ysize..ysize],t=-a-hmax..-a,frames=1

00,numpoints=2,color=violet,thickness=2):" }{TEXT -1 62 " Animated ver

tical line at the second point on the secant line" }}}{EXCHG {PARA 0 "

> " 0 "" {MPLTEXT 1 0 21 "p6:=display(\{p4,p5\}):" }{TEXT -1 43 " Put \+

the two right-side animations together" }}}{EXCHG {PARA 0 "> " 0 "" 

{MPLTEXT 1 0 96 "p7:=animate(f(a)+D(f)(a)*(x-a),x=xmin..xmax,t=0..1,fr

ames=50,numpoints=2,color=red,thickness=2):" }{TEXT -1 79 " A trivial \+

animation which displays the tangent line by itself for a short time" 

}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "p8:=animate(f(a)+((f(t)-

f(a))/(t-a))*(x-a), x=xmin..xmax, t=a-hmax..a,frames=100,numpoints=2,c

olor=red): " }{TEXT -1 36 "Animated secant lines from the left." }}}

{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "p9:=animate([t,f(t)+x,x=-ys

ize..ysize],t=a-hmax..a,frames=100,numpoints=2,color=violet,thickness=

2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "p10:=display(\{p8,p9

\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "p11:=display([p6,p7

,p10,p7],insequence=true):" }{TEXT -1 38 " Display one animation after

 the other" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "display(\{p1,

p2,p3,p11\}); " }{TEXT -1 74 "Display the unchanging parts of the grap

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