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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "Lab 11 Maple Activities fo
r October 17:  (Lesson 7 - Derivatives of Piecewise Functions)" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 384 "I
n this lab activity, we will use Maple to find the derivative of piece
wise functions.  Unfortunately, as you will see, Maple V Release 5, wi
ll not give us the correct answer for these problems.  However, you ma
y use Maple 6 in the Newton Lab (UH 1000) in order to find the derivat
ive of piecewise functions.  This new release of Maple will give the c
orrect answer for these problems." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }
{TEXT 264 0 "" }{TEXT 265 8 "Examples" }{TEXT 266 0 "" }{TEXT -1 40 " \+
 Differentiate the following functions." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "1.  " }{TEXT 256 1 "f" }
{TEXT -1 1 "(" }{TEXT 257 1 "x" }{TEXT -1 4 ") = " }{XPPEDIT 18 0 "abs
(x-4);" "6#-%$absG6#,&%\"xG\"\"\"\"\"%!\"\"" }{TEXT -1 1 " " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f := x -> abs(x-4);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 8 "D(f)(x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 64 "This answer does not make any sense.
  Let's define the function " }{TEXT 258 1 "f" }{TEXT -1 38 " as the p
iecewise function that it is:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 48 "f := x -> piecewise(x>=4, x - 4, x<4, -(x - 4));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "D(f)(x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 259 5 "NOTE:" }{TEXT -1 17 "  Thi
s answer is " }{TEXT 260 0 "" }{TEXT 261 3 "not" }{TEXT 262 0 "" }
{TEXT -1 41 " correct because we saw in lecture that  " }{TEXT 263 1 "
f" }{TEXT -1 91 " '(4) is undefined.  Redo this problem using Maple 6 \+
in order to obtain the correct answer." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "2.  " }{TEXT 267 1 "g" }
{TEXT -1 1 "(" }{TEXT 268 1 "x" }{TEXT -1 4 ") = " }{XPPEDIT 18 0 "PIE
CEWISE([3*x^2-2*x+20, -2 <= x],[8-14*x, x < -2]);" "6#-%*PIECEWISEG6$7
$,(*&\"\"$\"\"\"*$%\"xG\"\"#F*F**&F-F*F,F*!\"\"\"#?F*1,$F-F/F,7$,&\"\"
)F**&\"#9F*F,F*F/2F,,$F-F/" }{TEXT -1 1 " " }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 61 "g := x -> piecewise(x>=-2, 3*x^2 - 2*x + 20, x<-2, \+
8 - 14*x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g(x);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "D(g)(x);" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 "As we saw in lectu
re, this answer is correct." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 269 17 "Practice Problems" }
{TEXT -1 64 "  Use Maple 6 to find the derivative of the following fun
ctions." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 4 "1.  " }{TEXT 270 1 "f" }{TEXT -1 1 "(" }{TEXT 271 1 "x" }
{TEXT -1 4 ") = " }{XPPEDIT 18 0 "PIECEWISE([x^2+5, x <= 3],[6*x-4, 3 \+
< x]);" "6#-%*PIECEWISEG6$7$,&*$%\"xG\"\"#\"\"\"\"\"&F+1F)\"\"$7$,&*&
\"\"'F+F)F+F+\"\"%!\"\"2F.F)" }{TEXT -1 1 " " }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 4 "2.  " }{TEXT 272 1 "g" }{TEXT -1 1 "(" }
{TEXT 273 1 "x" }{TEXT -1 4 ") = " }{XPPEDIT 18 0 "PIECEWISE([2*x^2+3,
 x < -1],[4*x+9, -1 <= x]);" "6#-%*PIECEWISEG6$7$,&*&\"\"#\"\"\"*$%\"x
GF)F*F*\"\"$F*2F,,$F*!\"\"7$,&*&\"\"%F*F,F*F*\"\"*F*1,$F*F0F," }{TEXT 
-1 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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