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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "f:=x -> x^3+Pi^2*x*(
sin(x)-cos(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6
$%)operatorG%&arrowGF(,&*$)9$\"\"$\"\"\"F1*()%#PiG\"\"#F1F/F1,&-%$sinG
6#F/F1-%$cosGF9!\"\"F1F1F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
120 "Common mistake was to write 'evalf(-Pi/2);', which just outputs t
he value of -Pi/2 in decimal form (-1.57...) instead of" }}{PARA 0 "" 
0 "" {TEXT -1 47 "the value of f(-Pi/2), which is what we wanted:" }}
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}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "The correct way is :" }}}{EXCHG 
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{TEXT -1 37 "We zoom in on the plot to see better:" }}}{EXCHG {PARA 0 
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80 "We can clearly see from the above plot that the function has 3 roo
ts (in [-4,4])" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "f(1/2)*f(
2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&#\"\"\"\"\")F&*&#F&\"\"#F&*
&)%#PiGF*F&,&-%$sinG6#F)F&-%$cosGF1!\"\"F&F&F&F&,&F'F&*(F*F&F,F&,&-F06
#F*F&-F3F9F4F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$!+s(QaG'!\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "S
ince f(0.5)f(2)<0 we deduce that the interval (0.5,2) contains the pos
itive root of f." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 131 "------------
---------------------------------------------------  PROBLEM 3 -------
-------------------------------------------------" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 15 "fsolve(f(x)=0);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"\"!F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 120 "'fsol
ve' gave us a root, but we wanted all 3, so now we'll explicitly tell \+
'fsolve', where to look for the other 2 roots" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 24 "fsolve(f(x)=0,x=0.5..2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+l\"GcX(!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 24 "fsolve(f(x)=0,x=-3..-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+:
jF]?!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "............ and that
 is the whole Maple lab report that you had to turn in." }}}}{MARK "24
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}