{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 260 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 268 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 272 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 276 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 280 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 282 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 283 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 284 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 285 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 286 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 287 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 288 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 289 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 290 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 291 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 292 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 293 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 294 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 295 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 296 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 297 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 298 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 299 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 300 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 301 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 302 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 303 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 121 "Lab 16 Maple Activities f or November 14: (Lesson 14 - Increasing and Decreasing Functions and \+ the First Derivative Test)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 134 "In this lab, we compare the graph of a function and th e graph of its first derivative in order to visualize the First Deriva tive Test." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 264 0 "" }{TEXT 265 8 "Examples" }{TEXT 266 0 "" }{TEXT -1 413 " Plot the following functions and its first derivative on one graph. Determine the interval(s) where the first derivative o f the function is positive and then verify that the graph of the funct ion is increasing on this (these) interval(s). Determine the interval (s) where the first derivative of the function is negative and then ve rify that the graph of the function is decreasing on this (these) inte rval(s)." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "1. " }{TEXT 267 1 "f" }{TEXT -1 1 "(" }{TEXT 268 1 "x" } {TEXT -1 4 ") = " }{XPPEDIT 18 0 "-2*x^2+12*x-19;" "6#,(*&\"\"#\"\"\"* $%\"xG\"\"#F&!\"\"*&\"#7F&F(F&F&\"#>F*" }{TEXT -1 1 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "a. Defin e the function using Maple syntax:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "f := x -> -2*x^2 + 12*x - 19;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "b. Check to see if \+ you defined the function correctly:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 60 "c. Plot the function and its first deriv ative on one graph:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plot ([f(x), D(f)(x)], x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 35 "d. You might to need restrict the " } {TEXT 256 1 "y" }{TEXT -1 33 " values on some of the functions:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot([f(x), D(f)(x)], x, y=- 20..20);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "e. Compare the graph of the function " }{TEXT 257 1 "f" }{TEXT -1 107 " with the sign of its first derivative: \"From the gra ph of the first derivative in green, we can see that " }{TEXT 258 1 "f " }{TEXT -1 3 " '(" }{TEXT 259 1 "x" }{TEXT -1 19 ") is positive when \+ " }{TEXT 260 1 "x" }{TEXT -1 54 " < 3. We can also see from the graph of the function " }{TEXT 261 1 "f" }{TEXT -1 127 " in red, that the f unction is increasing on this interval.\" \"From the graph of the fir st derivative in green, we can see that " }{TEXT 256 1 "f" }{TEXT -1 3 " '(" }{TEXT 257 1 "x" }{TEXT -1 19 ") is negative when " }{TEXT 258 1 "x" }{TEXT -1 54 " > 3. We can also see from the graph of the f unction " }{TEXT 259 1 "f" }{TEXT -1 59 " in red, that the function is decreasing on this interval.\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "f. Use Maple to solve the inequalit y " }{TEXT 262 1 "f" }{TEXT -1 3 " '(" }{TEXT 263 1 "x" }{TEXT -1 6 ") > 0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "solve(D(f)(x)>0); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "g. Use Maple to solve the inequality " }{TEXT 256 1 "f" }{TEXT -1 3 " '(" }{TEXT 257 1 "x" }{TEXT -1 6 ") < 0:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 17 "solve(D(f)(x)<0);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "2. " }{TEXT 269 1 "f" } {TEXT -1 1 "(" }{TEXT 270 1 "x" }{TEXT -1 4 ") = " }{XPPEDIT 18 0 "4*x ^3-15*x^2-18*x+10;" "6#,**&\"\"%\"\"\"*$%\"xG\"\"$F&F&*&\"#:F&*$F(\"\" #F&!\"\"*&\"#=F&F(F&F.\"#5F&" }{TEXT -1 1 " " }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "a. Define the function using Maple syntax:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "b . Check to see if you defined the function correctly:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "c. Plot the function and its f irst derivative on one graph:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "d. You might to need restrict the " }{TEXT 256 1 "y" } {TEXT -1 33 " values on some of the functions:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 38 "e. Compare the graph of the function " } {TEXT 257 1 "f" }{TEXT -1 39 " with the sign of its first derivative: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "f. Use Maple to solve the inequality " }{TEXT 262 1 "f" }{TEXT -1 3 " '(" }{TEXT 263 1 "x" }{TEXT -1 6 ") > 0:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 38 "g. Use Maple to solve the inequality " } {TEXT 256 1 "f" }{TEXT -1 3 " '(" }{TEXT 257 1 "x" }{TEXT -1 6 ") < 0: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "3. " }{TEXT 271 1 "y " }{TEXT -1 3 " = " }{XPPEDIT 18 0 "x^4+8*x^3;" "6#,&*$%\"xG\"\"%\"\" \"*&\"\")F'*$F%\"\"$F'F'" }{TEXT -1 1 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "a. Define the function u sing Maple syntax:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "b. Check to see if you defined the function correctly:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "c. Plot the function and its f irst derivative on one graph:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "d. You might to need restrict the " }{TEXT 256 1 "y" } {TEXT -1 33 " values on some of the functions:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 38 "e. Compare the graph of the function " } {TEXT 273 1 "y" }{TEXT -1 39 " with the sign of its first derivative: " }{TEXT 272 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 38 "f. Use Maple to solve the inequality " }{TEXT 274 1 "y" }{TEXT -1 3 " '(" }{TEXT 259 1 "x" }{TEXT -1 6 ") > 0:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "g. Use Maple to solve th e inequality " }{TEXT 275 1 "y" }{TEXT -1 3 " '(" }{TEXT 257 1 "x" } {TEXT -1 6 ") < 0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "4. \+ " }{TEXT 276 1 "s" }{TEXT -1 1 "(" }{TEXT 277 1 "t" }{TEXT -1 4 ") = \+ " }{XPPEDIT 18 0 "sqrt(2*t^2+3);" "6#-%%sqrtG6#,&*&\"\"#\"\"\"*$%\"tG \"\"#F)F)\"\"$F)" }{TEXT -1 1 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "a. Define the function using Mapl e syntax:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "b. Check to see if you defined the function correctly:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 60 "c. Plot the function and its first deriv ative on one graph:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "d. You might to need restrict the " }{TEXT 256 1 "y" }{TEXT -1 33 " val ues on some of the functions:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "e. Compare the graph of the function " }{TEXT 278 1 "s" }{TEXT -1 39 " with the sign of its first derivative:" }{TEXT 259 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "f. Use Maple to solve the inequality " }{TEXT 279 1 "s" }{TEXT -1 3 " '(" }{TEXT 280 1 "t" }{TEXT -1 6 ") > 0:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 38 "g. Use Maple to solve the inequality " } {TEXT 281 1 "s" }{TEXT -1 3 " '(" }{TEXT 282 1 "t" }{TEXT -1 6 ") < 0: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "5. " }{TEXT 283 1 "g " }{TEXT -1 1 "(" }{TEXT 284 1 "u" }{TEXT -1 4 ") = " }{XPPEDIT 18 0 " (u^2+4)/((u+1)^3);" "6#*&,&*$%\"uG\"\"#\"\"\"\"\"%F(F(*$,&F&F(\"\"\"F( \"\"$!\"\"" }{TEXT -1 1 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 43 "a. Define the function using Maple synta x:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "b. Check to see i f you defined the function correctly:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 60 "c. Plot the function and its first derivative on \+ one graph:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "d. You m ight to need restrict the " }{TEXT 256 1 "y" }{TEXT -1 33 " values on \+ some of the functions:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "e. Compare the graph of the function " }{TEXT 285 1 "g" }{TEXT -1 39 " with the sign of its first derivative:" }{TEXT 259 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "f. Use Maple to solve the inequality " }{TEXT 286 1 "g" }{TEXT -1 3 " ' (" }{TEXT 287 1 "u" }{TEXT -1 6 ") > 0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 38 "g. Use Maple to solve the inequality " }{TEXT 288 1 "g" }{TEXT -1 3 " '(" }{TEXT 289 1 "u" }{TEXT -1 6 ") < 0:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "6. " }{TEXT 290 1 "y" } {TEXT -1 3 " = " }{XPPEDIT 18 0 "x^4-8*x^2;" "6#,&*$%\"xG\"\"%\"\"\"*& \"\")F'*$F%\"\"#F'!\"\"" }{TEXT -1 1 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "a. Define the function u sing Maple syntax:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "b. Check to see if you defined the function correctly:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "c. Plot the function and its f irst derivative on one graph:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "d. You might to need restrict the " }{TEXT 256 1 "y" } {TEXT -1 33 " values on some of the functions:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 38 "e. Compare the graph of the function " } {TEXT 260 1 "y" }{TEXT -1 39 " with the sign of its first derivative: " }{TEXT 259 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 38 "f. Use Maple to solve the inequality " }{TEXT 261 1 "y" }{TEXT -1 3 " '(" }{TEXT 258 1 "x" }{TEXT -1 6 ") > 0:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "g. Use Maple to solve th e inequality " }{TEXT 262 1 "y" }{TEXT -1 3 " '(" }{TEXT 257 1 "x" } {TEXT -1 6 ") < 0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "7. \+ " }{TEXT 291 1 "h" }{TEXT -1 1 "(" }{TEXT 292 1 "x" }{TEXT -1 4 ") = \+ " }{XPPEDIT 18 0 "x^2/(sqrt(x+7));" "6#*&%\"xG\"\"#-%%sqrtG6#,&F$\"\" \"\"\"(F*!\"\"" }{TEXT -1 1 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 43 "a. Define the function using Maple s yntax:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "b. Check to se e if you defined the function correctly:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 60 "c. Plot the function and its first derivative on \+ one graph:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "d. You m ight to need restrict the " }{TEXT 293 1 "y" }{TEXT -1 33 " values on \+ some of the functions:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "e. Compare the graph of the function " }{TEXT 294 1 "h" }{TEXT -1 39 " with the sign of its first derivative:" }{TEXT 259 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "f. Use Maple to solve the inequality " }{TEXT 295 1 "h" }{TEXT -1 3 " ' (" }{TEXT 258 1 "x" }{TEXT -1 6 ") > 0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 38 "g. Use Maple to solve the inequality " }{TEXT 296 1 "h" }{TEXT -1 3 " '(" }{TEXT 257 1 "x" }{TEXT -1 6 ") < 0:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "8. " }{TEXT 298 1 "f" } {TEXT -1 1 "(" }{TEXT 297 1 "t" }{TEXT -1 4 ") = " }{XPPEDIT 18 0 "2/( (5-t^3)^3);" "6#*&\"\"#\"\"\"*$,&\"\"&F%*$%\"tG\"\"$!\"\"\"\"$F," } {TEXT -1 1 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "a. Define the function using Maple syntax:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "b. Check to see if you d efined the function correctly:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "c. Plot the function and its first derivative on one gra ph:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "d. You might to n eed restrict the " }{TEXT 256 1 "y" }{TEXT -1 33 " values on some of t he functions:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "e. Compare the graph of the function " }{TEXT 299 1 "f" }{TEXT -1 39 " \+ with the sign of its first derivative:" }{TEXT 257 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "f. Use M aple to solve the inequality " }{TEXT 300 1 "f" }{TEXT -1 3 " '(" } {TEXT 260 1 "t" }{TEXT -1 6 ") > 0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 38 "g. Use Maple to solve the inequality " }{TEXT 301 1 "f" }{TEXT -1 3 " '(" }{TEXT 262 1 "t" }{TEXT -1 6 ") < 0:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "9. " }{TEXT 302 1 "y" }{TEXT -1 3 " = " }{TEXT 303 1 "x" }{TEXT -1 3 " + " }{XPPEDIT 18 0 "4/(x^2);" "6#*&\"\"%\"\"\"*$%\"xG\" \"#!\"\"" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 43 "a. Define the function using Maple synta x:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "b. Check to see i f you defined the function correctly:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 60 "c. Plot the function and its first derivative on \+ one graph:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "d. You m ight to need restrict the " }{TEXT 256 1 "y" }{TEXT -1 33 " values on \+ some of the functions:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "e. Compare the graph of the function " }{TEXT 260 1 "y" }{TEXT -1 39 " with the sign of its first derivative:" }{TEXT 259 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "f. Use Maple to solve the inequality " }{TEXT 261 1 "y" }{TEXT -1 3 " ' (" }{TEXT 258 1 "x" }{TEXT -1 6 ") > 0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 38 "g. Use Maple to solve the inequality " }{TEXT 262 1 "y" }{TEXT -1 3 " '(" }{TEXT 257 1 "x" }{TEXT -1 6 ") < 0:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 }