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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

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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" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "p1:=pl

ot(f,xmin..xmax,color=black): " }{TEXT -1 24 "Plot the function itself

" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "p2:=plot([a,f(a)-x,x=-y

size..ysize],numpoints=2,color=violet): " }{TEXT -1 19 "A vertical lin

e 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,numpoin

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"> " 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 34 "Animated secant lines.  Note that " }{TEXT 259 1 "t" }

{TEXT -1 64 " is deliberately the negative of what it should be, so th

at the " }{TEXT 260 1 "t" }{TEXT -1 31 " range goes from left to right

." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "p5:=animate([-t,f(-t)

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thickness=2):" }{TEXT -1 62 " Animated vertical line at the second poi

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