{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 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 0 1 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 "" -1 268 "" 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 "" -1 291 "" 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 "" -1 302 "" 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 }{CSTYLE "" -1 304 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 305 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 306 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 307 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 308 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 315 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 316 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 317 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 319 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 321 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 322 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 323 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 324 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 331 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 332 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 333 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 334 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 335 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 336 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 337 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 338 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 345 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 346 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 347 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 348 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 349 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 350 "" 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 64 "Lab 17 Maple Activities fo r December 5: (Lesson 15 - Concavity)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 175 "In this lab, we compare the graph of a f unction and the graph of its second derivative in order to compare the concavity of the function and the sign of its second derivative." }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 256 0 "" }{TEXT 257 8 "Examples" }{TEXT 258 0 "" }{TEXT -1 428 " Plot the following functions and its second derivative on one graph. Determine the interval(s) where the second derivative of the functio n is positive and then verify that the graph of the function is concav ed upward on this (these) interval(s). Determine the interval(s) wher e the second derivative of the function is negative and then verify th at the graph of the function is concaved downward on this (these) inte rval(s)." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "1. " }{TEXT 259 1 "f" }{TEXT -1 1 "(" }{TEXT 260 1 "x" } {TEXT -1 4 ") = " }{XPPEDIT 18 0 "x^3+10*x^2+25*x-50;" "6#,**$)%\"xG\" \"$\"\"\"\"\"\"*$)F&\"\"#F(\"#5F&\"#D!#]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 -> x^3+10*x^2+25*x-50;" }}}{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 61 "c. Plot the function and its second deri vative on one graph:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plo t([f(x), (D@@2)(f)(x)], x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 35 "d. You might to need restrict the " } {TEXT 269 1 "y" }{TEXT -1 33 " values on some of the functions:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plot([f(x), (D@@2)(f)(x)], x , y=-200..800);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "e. Compare the graph of the function " }{TEXT 270 1 "f" }{TEXT -1 109 " with the sign of its second derivative: \"From \+ the graph of the second derivative in green, we can see that " }{TEXT 271 1 "f" }{TEXT -1 4 " ''(" }{TEXT 259 1 "x" }{TEXT -1 19 ") is posit ive when " }{TEXT 260 1 "x" }{TEXT -1 78 " > - 10/3 (from Maple below) . We can also see from the graph of the function " }{TEXT 261 1 "f" } {TEXT -1 133 " in red, that the function is concaved upward on this in terval.\" \"From the graph of the second derivative in green, we can \+ see that " }{TEXT 272 1 "f" }{TEXT -1 4 " ''(" }{TEXT 273 1 "x" } {TEXT -1 19 ") is negative when " }{TEXT 274 1 "x" }{TEXT -1 59 " < - \+ 10/3. We can also see from the graph of the function " }{TEXT 259 1 " f" }{TEXT -1 66 " in red, that the function is concaved downward on th is interval.\"" }}}{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 4 " ''(" }{TEXT 263 1 "x" }{TEXT -1 6 ") > 0:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "solve((D@@2)(f)(x)>0);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "g. Use Maple to solve the inequality " }{TEXT 275 1 "f" }{TEXT -1 4 " ' '(" }{TEXT 276 1 "x" }{TEXT -1 6 ") < 0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "solve((D@@2)(f)(x)<0);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "2. " }{TEXT 277 1 "y" } {TEXT -1 3 " = " }{XPPEDIT 18 0 "3*x^5-5*x^3;" "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 using M aple 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 61 "c. Plot the function and its second deri vative 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 261 1 "y" }{TEXT -1 33 " va lues 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 291 1 "y" }{TEXT -1 41 " with the sign of its second derivative: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "f. Use M aple to solve the inequality " }{TEXT 292 1 "y" }{TEXT -1 4 " ''(" } {TEXT 260 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 293 1 "y" }{TEXT -1 4 " ''(" }{TEXT 268 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 294 1 "s" } {TEXT -1 1 "(" }{TEXT 295 1 "t" }{TEXT -1 4 ") = " }{XPPEDIT 18 0 "t^5 -5*t^4+t;" "6#,(*$)%\"tG\"\"&\"\"\"\"\"\"*$)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 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 61 "c. Plot the function and its second 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 res trict the " }{TEXT 302 1 "y" }{TEXT -1 33 " values on some of the func tions:" }}}{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 303 1 "s" }{TEXT -1 41 " with the sign of its second derivative: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 38 "f. Use Maple to solve the inequality " }{TEXT 304 2 "s " }{TEXT -1 3 "''(" }{TEXT 305 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 s olve the inequality " }{TEXT 306 1 "s" }{TEXT -1 4 " ''(" }{TEXT 307 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 "4. " }{TEXT 308 1 "y" }{TEXT -1 3 " = " }{XPPEDIT 18 0 "(u^2-9)^2; " "6#*$),&*$)%\"uG\"\"#\"\"\"\"\"\"!\"*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 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 corr ectly:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 61 "c. Plot the fu nction and its second 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 315 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 316 1 "y" }{TEXT -1 41 " with the sign of its se cond derivative: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 38 "f. Use Maple to solve the inequality " }{TEXT 317 1 "y" }{TEXT -1 4 " ''(" }{TEXT 321 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 th e inequality " }{TEXT 319 1 "y" }{TEXT -1 4 " ''(" }{TEXT 322 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 "5. \+ " }{TEXT 323 1 "g" }{TEXT -1 1 "(" }{TEXT 324 1 "w" }{TEXT -1 4 ") = \+ " }{XPPEDIT 18 0 "(5-3*w)^4;" "6#*$),&\"\"&\"\"\"%\"wG!\"$\"\"%\"\"\" " }{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 61 "c. Plot the function and its second derivative on one gr aph:" }}}{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 331 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 332 1 "g" }{TEXT -1 41 " \+ with the sign of its second derivative: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "f. Use Maple to solve th e inequality " }{TEXT 333 1 "g" }{TEXT -1 4 " ''(" }{TEXT 335 1 "w" } {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 334 1 "g" }{TEXT -1 4 " ' '(" }{TEXT 336 1 "w" }{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 337 1 "h" }{TEXT -1 1 "(" }{TEXT 338 1 "x" }{TEXT -1 4 ") = " }{XPPEDIT 18 0 "x/(x^2-1);" "6#*&%\"xG\"\"\", &*$)%\"xG\"\"#\"\"\"\"\"\"!\"\"F,!\"\"" }}}{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 61 "c. Plot the function and its s econd 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 350 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 345 1 "h" }{TEXT -1 41 " with the sign of its second derivative: " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "f. Use Maple to solve the inequality " }{TEXT 346 1 "h" }{TEXT -1 4 " ''(" }{TEXT 347 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 348 1 "h" }{TEXT -1 4 " ''(" }{TEXT 349 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 }