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'y&*\\V\"F07$$!3!******\\!)H%*\\\"F0$\"3-z8:;BjG()!#=7$$!3/+++vl[p8F0$ \"32glMhT.+YFeo7$$!3\"******\\>iUC\"F0$\"3L2Z$=Cdc$>Feo7$$!3-++DhkaI6F 0$\"3LM7]%y&>N`!#>7$$!3s******\\XF`**Feo$\"3_(eGmh,'Rl!#A7$$!3u******* >#z2))Feo$\"3i&RQUtAY4%Fep7$$!3S++]7RKvuFeo$\"31z*z\">UF^F0 7$$\"3]****\\(QIKH\"Feo$\"31ixwfi!eQ#F07$$\"38****\\7:xWCFeo$\"3\\QS&* z#>)=FF07$$\"3E,++vuY)o$Feo$\"31\">X&3%fj0$F07$$\"3!z******4FL(\\Feo$ \"3?ZB#[%z)*oLF07$$\"3A)****\\d6.B'Feo$\"3)4h(HCGDFOF07$$\"3s****\\(o3 lW(Feo$\"3'Hiy&Q+/@QF07$$\"35*****\\A))oz)Feo$\"3MRJYRrJeRF07$$\"3e*** ***Hk-,5F0$\"39hHCQo****RF07$$\"36+++D-eI6F0$\"3E*>;c')>m%RF07$$\"3u** *\\(=_(zC\"F0$\"3A'yQEXw-!QF07$$\"3M+++b*=jP\"F0$\"3U4/zj$f=_$F07$$\"3 g***\\(3/3(\\\"F0$\"3ZL`,M,\"f8$F07$$\"33++vB4JB;F0$\"3_(H;P*QG#f#F07$ $\"3u*****\\KCnu\"F0$\"39VaYTp$3\">F07$$\"3s***\\(=n#f(=F0$\"3VQZ%GY/i -\"F07$$\"3P+++!)RO+?F0$!3Gtj'o$\\hwKFbs7$$\"30++]_!>w7#F0$!3!fk07pp$[ 7F07$$\"3O++v)Q?QD#F0$!3au%*RiXG(o#F07$$\"3G+++5jypBF0$!3%[8u&oN4*>%F0 7$$\"3<++]Ujp-DF0$!33,(\\4%>_nhF07$$\"3++++gEd@EF0$!3%[2@cc:C:)F07$$\" 39++v3'>$[FF0$!3]Rn\")e:Q^5F37$$\"37++D6EjpGF0$!35=Y^*y#>-8F37$$\"\"$F *$F3F*-%'COLOURG6&%$RGBG$F*F*F`[l$\"*++++\"!\")-%+AXESLABELSG6$Q\"x6\" Q\"yFh[l-%%VIEWG6$;F(Fiz;$!\"%F*$\"\")F*" 1 2 0 1 10 0 2 6 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "Dr. John Pais, Mathematics Depa rtment-MICDS" }}{PARA 0 "" 0 "" {TEXT -1 45 "E-mail: pais@micds.org or pais@kinetigram.com" }}{PARA 0 "" 0 "" {TEXT -1 33 "URL: http://kine tigram.com/micds" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 " " 0 "" {TEXT -1 30 "Compile Secant Line Movie Code" }}{PARA 0 "" 0 "" {TEXT 270 110 "Click in red area and press [Enter] to compile code.\nN ext, close this section and proceed to the next section." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9732 "restart:\nwith(plottools):\nSecan tLineMovie:=proc(expr,time,frame)\nlocal m,i,xleft,xright,yint_xleft_s tr,yint_xright_str,\nelapsed_time,time_text,elapsed_time_str,dist_trav ,dist_trav_str,\nvelocity,velocity_str,tsf_str,rp,endcolor,endlinestyl e,h,h_approx,\nh_txt,h_txt_digit,h_txt_t,t1,t2,y1,y2,sec_xright,tsf_xr ight_str,\nf,IN,tif,tsf,maincolor,movie_frame,reversemovie_frame,Secan tLine:\nf:=unapply(expr,x);\nIN:=unapply(unapply(normal(f(x)-D(f)(x)*x ),x),f):\ntif:=unapply(IN(f)(t),t):\ntsf:=unapply(D(f)(t),t):\nDigits: =6:\nm:=21:\nfor i from 1 to m do\nxright:=time:\ntime_text:=convert(t ime,string):\nif xright >= 2 then\nsec_xright:=xright + .2:\nelif 1 <= xright and xright < 2 then\nsec_xright:=2:\nelif 0 <= xright and xrig ht < 1 then\nsec_xright:=1.4:\nelif -1 <= xright and xright < 0 then\n sec_xright:=0:\nelif -2 <= xright and xright < -1 then \nsec_xright:=- .6:\nelif xright < -2 then \nsec_xright:=xright + .2:\nfi:\nh:=(sec_xr ight-xright)*(1.2)^(-i+1):\nh_approx:=evalf(trunc(100*h)/100,2):\nif h _approx >= .1 then\nh_txt:=convert(h_approx,string):\nelse\nh_txt_digi t:=trunc(100*h_approx):\nh_txt:=`.0`||h_txt_digit:\nfi:\nt1:=evalf(xri ght):\nt2:=evalf(xright+h):\ny1:=evalf(f(xright)):\ny2:=evalf(f(xright +h)):\nyint_xright_str:=convert(evalf(IN(f)(xright),3),string):\ntsf_x right_str:=convert(evalf(D(f)(xright),3),string):\nmaincolor:=navy:\ne ndcolor:=red:\nrp[1]:=plot(f(t),t=-3..3.4,y=-3...7,\n#rp[1]:=plot(f(t) ,t=-2..2,y=-8...8,\n labels=[``,``],\n color=blu e,linestyle=1):\nrp[2]:=plot([[t1,y1],[t2,y1]],linestyle=1,color=mainc olor):\nrp[3]:=plot([[t2,y1],[t2,y2]],linestyle=1,color=maincolor):\nr p[4]:=plot([[t1,y1],[t2,y2]],linestyle=1,color=maincolor):\nrp[5]:=plo t(((y2-y1)/(t2-t1))*t+f(t1)-((y2-y1)/(t2-t1))*t1,\n t=t 1..5,y=f(t1)...5,color=maincolor):\nif h_approx >= 0.3 then\nh_txt_t:= (t1+t2)/2:\nelse\nh_txt_t:=t2+0.25:\nfi:\nrp[6]:=plots[textplot]([h_tx t_t,0.3,h_txt],\n font=[HELVETICA,DEFAULT,10], \n color=maincolor,align=\{ABOVE,CENTER\}):\nrp [7]:=plots[textplot]([t2+0.05,(y1+y2)/2,\n `f(x + `||h_txt||`) - f(x)`],\n font=[HELVETICA,DEF AULT,10],\n color=maincolor,align=\{RIGHT\}): \+ \nrp[8]:=plots[textplot]([0,0,``]):\n\n# end movie_frame[i] for i < m \nrp[9]:=plot([[xright,f(xright)],[xright,IN(f)(xright)]],\n \+ linestyle=1,color=red):\n#rp[10]:=plot([[xright,IN(f)(xright)],[0,I N(f)(xright)]],\n# linestyle=1,color=red):\nrp[10]:=plot([ [0,IN(f)(xright)],[-f(xright),xright]],\n linestyle=1,col or=red):\nrp[11]:=plot([[0,IN(f)(xright)],[xright,f(xright)]],\n \+ linestyle=1,color=red):\n# movie_frame[i] for i < m\n#rp[12]:= plots[textplot]([1.15,6.8,`3`],\nrp[12]:=plots[textplot]([1.15,6.8,``] ,\n font=[HELVETICA,DEFAULT,10],\n \+ color=maincolor,align=\{BELOW,RIGHT\}): \+ \n#rp[13]:=plots[textplot]([0.1,6.5,`y = f(x) = -x + 3x + 2`],\nrp[1 3]:=plots[textplot]([0.1,6.5,``],\n font=[HELVE TICA,DEFAULT,12],\n color=maincolor,align=\{RIG HT\}): \nif i < m then\nrp[14]:=plots[textplot]([0.1,5.5,`secant f (x + `||h_txt||`) - f(x)`],\n font=[HELVETICA,D EFAULT,12],\n color=maincolor,align=\{RIGHT\}): \nrp[15]:=plots[textplot]([0.2,5.3,`slope`],\n \+ font=[HELVETICA,DEFAULT,12],\n color=maincolor ,align=\{BELOW,RIGHT\}):\nrp[16]:=plots[textplot]([0.8,5.35,`=`],\n \+ font=[HELVETICA,DEFAULT,12],\n \+ color=maincolor,align=\{BELOW,RIGHT\}):\n\nrp[17]:=plot([[1.05,5. 2],[2.3,5.2]],linestyle=1,color=maincolor):\nrp[18]:=plots[textplot]([ 1.7,5.1,h_txt],\n font=[HELVETICA,DEFAULT,12], \n color=maincolor,align=\{BELOW,CENTER\}): \ne lif i = m and 0 <= xright then\nrp[14]:=plots[textplot]([0,0,``]):\nrp [15]:=plots[textplot]([0.2,5.35,`slope`],\n fon t=[HELVETICA,DEFAULT,12],\n color=endcolor,alig n=\{BELOW,RIGHT\}):\nrp[16]:=plots[textplot]([0.8,5.35,`=`],\n \+ font=[HELVETICA,DEFAULT,12], \+ \+ color=endcolor,align=\{BELOW,RIGHT\}):\nrp[17]:=plots[textplot]([0,0,` `]):\nrp[18]:=plots[textplot]([1.05,5.35,tsf_xright_str],\n \+ font=[HELVETICA,DEFAULT,12],\n col or=endcolor,align=\{BELOW,RIGHT\}): \nelif i = m and xright < 0 then\n rp[14]:=plots[textplot]([0,0,``]):\nrp[15]:=plots[textplot]([-1.6,5.35 ,`slope`],\n font=[HELVETICA,DEFAULT,12],\n \+ color=endcolor,align=\{BELOW,RIGHT\}):\nrp[16]:=pl ots[textplot]([-1.0,5.35,`=`],\n font=[HELVETIC A,DEFAULT,12], \+ \+ colo r=endcolor,align=\{BELOW,RIGHT\}):\nrp[17]:=plots[textplot]([0,0,``]): \nrp[18]:=plots[textplot]([-0.8,5.35,tsf_xright_str],\n \+ font=[HELVETICA,DEFAULT,12],\n color=e ndcolor,align=\{BELOW,RIGHT\}): \nfi:\nif i = 1 and 0 <= xright then\n rp[19]:=plots[textplot]([1.0,-1.0,\n `Begin x \+ = `||time_text],\n font=[HELVETICA,DEFAULT,12], \n color=blue,align=\{CENTER\}):\nelif i = 1 an d xright < 0 then \nrp[19]:=plots[textplot]([-1.0,-1.0,\n \+ `Begin x = `||time_text],\n font=[H ELVETICA,DEFAULT,12],\n color=blue,align=\{CENT ER\}):\nelif 1 < i and 0 <= xright then\nrp[19]:=plots[textplot]([1.0, -1.0,\n `x = `||time_text],\n \+ font=[HELVETICA,DEFAULT,12],\n color=blue ,align=\{CENTER\}):\nelif 1 < i and xright < 0 then\nrp[19]:=plots[tex tplot]([-1.0,-1.0,\n `x = `||time_text],\n \+ font=[HELVETICA,DEFAULT,12],\n \+ color=blue,align=\{CENTER\}):\nfi:\n# end movie_frame[i] for i < m \nrp[20]:=plot(tsf(t1)*t+tif(t1),t=-4..4,color=red):\n# movie_frame[i] for i < m\nif xright = -1 and i = m then\n#rp[21]:=plot(tsf(t1+.1)*t+ tif(t1+.1),t=-4..4,thickness=3,color=red):\nrp[21]:=plot([[-3.5,.01],[ 3.6,.01]],thickness=2,color=red):\nelse\nrp[21]:=plots[textplot]([0,0, ``]):\nfi:\nrp[22]:=plot([[0,f(xright)],[xright,f(xright)]], \+ color=blue,linestyle=3);\nrp[23]:=plot([[xright, 0],[xright,f(xright)]], color=blue,line style=3);\nrp[24]:=plot([[0,y2],[t2,y2]],linestyle=3,color=maincolor): \nrp[25]:=plot([[t2,0],[t2,y1]],linestyle=3,color=maincolor):\n# end m ovie_frame[i] for i < m\nif t1 <= 0 and tsf(t1) <= 0 then\n rp[26]:=pl ots[textplot]([t1,f(t1)-2.0,`tangent`],\n font =[HELVETICA,DEFAULT,12],\n color=endcolor,alig n=\{BELOW,LEFT\}):\nelif t1 <= 0 and tsf(t1) > 0 then\n rp[26]:=plots[ textplot]([t1,f(t1)+2.0,`tangent`],\n font=[HE LVETICA,DEFAULT,12],\n color=endcolor,align=\{ ABOVE,LEFT\}):\nelif t1 > 0 and tsf(t1) <= 0 then\n rp[26]:=plots[text plot]([t1,f(t1)+2.0,`tangent`],\n font=[HELVET ICA,DEFAULT,12],\n color=endcolor,align=\{ABOV E,RIGHT\}):\nelif t1 > 0 and tsf(t1) > 0 then\n rp[26]:=plots[textplot ]([t1,f(t1)+2.0,`tangent`],\n font=[HELVETICA, DEFAULT,12],\n color=endcolor,align=\{ABOVE,CE NTER\}):\nfi:\nrp[27]:=plots[textplot]([t2+0.05,tif(t2)+(f(t2)-tif(t2) )/2,\n `tangent triangle`],\n \+ font=[HELVETICA,DEFAULT,12],\n color=e ndcolor,align=\{BELOW,RIGHT\}): \nif i =1 then\nmovie_frame [i]:=plots[display](\n [seq(rp[j],j=1..8),\n \+ seq(rp[j],j=12..19),\n seq(rp[j],j=21..25)]): \nelif 1 < i and i < m then\nmovie_frame[i]:=plots[display](\n \+ [seq(rp[j],j=1..7),\n seq(rp[j],j=12..19),\n seq(rp[j],j=21..25)]):\nelse\nmovie_frame[i]:=plots[ display](\n [seq(rp[j],j=1..1),\n seq (rp[j],j=12..23)\n\n # seq(rp[j],j=19..23),\n \+ # seq(rp[j],j=20..23),\n # seq(rp[j],j=26..26) \n]):\nfi:\n#reversemovie_frame[m-(i-1)]:=plots[display]([seq(rp[j],j= 0..8)]): \nod:\nif frame = 0 then\n# Create Maple movie.\nSecantLine[ frame]:=\n plots[display]([movie_frame[1],movie_frame[1],movie_frame[1 ],\n seq(movie_frame[j],j=1..m), \+ \+ \+ \+ movie_frame[m],mo vie_frame[m],movie_frame[m]],\n #seq(reversemovie_fram e[j],j=1..m),\n insequence = true,\n # scaling=constrained,\n #labels=[``,``],\n \+ xtickmarks=5,ytickmarks=4,\n view=[-3..3.4,-3..7], \n titlefont=[HELVETICA,DEFAULT,14],\n \+ title=`Slope of Tangent to Curve`):\nelse\n# Create individual frames to export to *.gifs for Java movie.\nSecantLine[frame]:=\n plots[disp lay]([movie_frame[frame]],\n #scaling=constrained,\n \+ #labels=[``,``],\n xtickmarks=4,ytickma rks=4,\n view=[-3..3.4,-3..7],\n title font=[HELVETICA,DEFAULT,14],\n title=`Slope of Secant \+ Line`):\nfi:\nSecantLine[frame]\nend:" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 21 "Run Secant Line Movie" }}{PARA 0 "" 0 "" {TEXT 258 54 "En ter the defining expression for the function f, and " }{TEXT -1 1 "\n " }{TEXT 259 54 "the x_val at which you want to compute the slope of f ." }{TEXT -1 1 " " }}{EXCHG {PARA 0 "" 0 "" {TEXT 257 0 "" }{MPLTEXT 1 0 65 "f:=x->x^2: \nx_val:=1:\n'f'(x)=f(x);\nSecantLineMovie(f(x),x_v al,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"fG6#%\"xG*$)F'\"\"#\"\" \"" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 {PLOTDATA 2 "6&-%(ANIMATE G6=79-%'CURVESG6%7S7$$!\"$\"\"!$\"\"*F.7$$!3ULLL8#)\\gG!#<$\"3-#>$[G+X #=)F47$$!3[mmma%=\"RFF4$\"332bp3*pF](F47$$!3ULLL@Uh-EF4$\"3?8l3&y+Ox'F 47$$!3OLLL\\^?lCF4$\"3a#e*HGkBxgF47$$!3Ymmme\"\\%GBF4$\"3H2b\\%[v;U&F4 7$$!3cLLL\\)e;?#F4$\"3oyx%))o,t%[F47$$!3G+++G[Pq?F4$\"3uIgTG>X'G%F47$$ !3RLLL02gM>F4$\"3mEWWwbFF47$$!3FLLL,6VP:F4$\"33EqM\"R%pjBF47$$!3%)** ***>z\"R*R\"F4$\"3#4(p^(Q(He>F47$$!39+++!o&yg7F4$\"3%G1$*3`!e*e\"F47$$ !3-+++3I@F6F4$\"313WSl\"41F\"F47$$!3OLLLDi\"f+\"F4$\"3ch))Q_u'=,\"F47$ $!3Womm'=Eoh)!#=$\"3mVC7`$p\\U(Fjp7$$!3?lmmY$y\\R(Fjp$\"33&)owu/doaFjp 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F/F2F3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&LimitG6$*&,&-%\"fG6#,&% \"xG\"\"\"%\"hGF.F.-F*6#F-!\"\"F.F/F2/F/\"\"!-F%6$,&*&\"\"#F.F-F.F.F/F .F3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&LimitG6$*&,&-%\"fG6#,&%\"xG \"\"\"%\"hGF.F.-F*6#F-!\"\"F.F/F2/F/\"\"!,$*&\"\"#F.F-F.F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/*&%MThus,~2~is~the~slope~of~the~tangent~lin e~to~G\"\"\"-%\"fG6#%\"xGF&*$)F*\"\"#F&/*&%#atGF&F*F&F&" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#%ZNotice~that~we~have~found~a~general~formula~fo r~the~slopeG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/*&%8of~the~tangent~li ne~to~G\"\"\"-%\"fG6#%\"xGF&*$)F*\"\"#F&%8~that~works~for~any~x~!G" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%!G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #%UDefinition~of~Tangent~Slope~Function~(Derivative):~~G" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/*&%*tsf(x)~=~G\"\"\"-%$f~'G6#%\"xGF&-%&LimitG6$ *&,&-%\"fG6#,&F*F&%\"hGF&F&-F1F)!\"\"F&F4F6/F4\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 265 9 "Exercises" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 266 11 "Exercise 1." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "n:=1: \nf:=x->x^3:\n``||n||`. `*'f'(x)=f(x),'`f '`'(x)=Limit(('f'(x+h)-'f'(x ))/h,h=0);\n`So, to get started `*'`f '`'(x)=Limit((f(x+h)-f(x))/h,h= 0);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/*&%$1.~G\"\"\"-%\"fG6#%\"xGF &*$)F*\"\"$F&/-%$f~'GF)-%&LimitG6$*&,&-F(6#,&F*F&%\"hGF&F&F'!\"\"F&F9F :/F9\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&%5So,~to~get~started~~ G\"\"\"-%$f~'G6#%\"xGF&-%&LimitG6$*&,&*$),&F*F&%\"hGF&\"\"$F&F&*$)F*F4 F&!\"\"F&F3F7/F3\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "" 0 "" {TEXT 267 11 "Exercise 2." }{TEXT -1 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 151 "n:=2:\nf:=x->x^3-x:\n``||n||`. `*' f'(x)=f(x),'`f '`'(x)=Limit(('f'(x+h)-'f'(x))/h,h=0);\n`So, to get sta rted `*'`f '`'(x)=Limit((f(x+h)-f(` x`))/h,h=0);\n" }}{PARA 11 "" 1 " " {XPPMATH 20 "6$/*&%$2.~G\"\"\"-%\"fG6#%\"xGF&,&*$)F*\"\"$F&F&F*!\"\" /-%$f~'GF)-%&LimitG6$*&,&-F(6#,&F*F&%\"hGF&F&F'F/F&F;F//F;\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/*&%5So,~to~get~started~~G\"\"\"-%$f~' G6#%\"xGF&-%&LimitG6$*&,,*$),&F*F&%\"hGF&\"\"$F&F&F*!\"\"F3F5*$)%#~xGF 4F&F5F8F&F&F3F5/F3\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 268 11 "Exercise 3." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 156 "n:=3:\nf:=x->-x^3+3*x+2:\n``||n| |`. `*'f'(x)=f(x),'`f '`'(x)=Limit(('f'(x+h)-'f'(x))/h,h=0);\n`So, to \+ get started `*'`f '`'(x)=Limit((f(x+h)-f(` x`))/h,h=0);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/*&%$3.~G\"\"\"-%\"fG6#%\"xGF&,(*$)F*\"\"$F& !\"\"*&F.F&F*F&F&\"\"#F&/-%$f~'GF)-%&LimitG6$*&,&-F(6#,&F*F&%\"hGF&F&F 'F/F&F=F//F=\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&%5So,~to~get~s tarted~~G\"\"\"-%$f~'G6#%\"xGF&-%&LimitG6$*&,,*$),&F*F&%\"hGF&\"\"$F&! \"\"*&F4F&F*F&F&*&F4F&F3F&F&*$)%#~xGF4F&F&*&F4F&F:F&F5F&F3F5/F3\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 269 11 "Exercise 4." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 350 "n:=4:\nf:=x->-x^3+3*x+2:\n``||n||`. Let`,'f'(x)=f(x) ,`then using the tangent slope function`;\n`found in Exercise 3 above, find the equation of the tangent line`;\n`to the curve below at each \+ of the following values:`;\n x = -2, -1.6, -1, 0, 1, 1.6, 2;`Also, acc urately sketch each tangent line on the plot below.`;\n\nplot(f(x),x=- 3..3,y=-4..8,color=blue);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%'4.~LetG /-%\"fG6#%\"xG,(*$)F(\"\"$\"\"\"!\"\"*&F,F-F(F-F-\"\"#F-%Fthen~using~t he~tangent~slope~functionG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%[ofound ~in~Exercise~3~above,~find~the~equation~of~the~tangent~lineG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%Tto~the~curve~below~at~each~of~the~followin g~values:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6)/%\"xG!\"#$!#;!\"\"F(\" \"!\"\"\"$\"#;F(\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%gnAlso,~accu rately~sketch~each~tangent~line~on~the~plot~below.G" }}{PARA 13 "" 1 " " {GLPLOT2D 486 486 486 {PLOTDATA 2 "6&-%'CURVESG6#7S7$$!\"$\"\"!$\"#? 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