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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 18 
"" 0 "" {TEXT -1 39 "Understanding max/min/inflection points" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "f
:=proc(x) arctan((2*x^2+1)/(x^2+2)) end;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "f(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "g:
=proc(x) diff(f(x),x) end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
15 "simplify(g(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "h:=p
roc(x) diff(g(x),x) end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "
h(x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "Exercise: (1) Can you de
termine which one is f, g  respectively?" }}{PARA 0 "" 0 "" {TEXT -1 
82 "(2) How are  the zeroes of function  g  related to the max/min of \+
the function  f?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plot(\{
f(x),g(x),h(x)\},x=-5..5,thickness=2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "Exercise: Use
 the function  f:=proc(x) arccot((2*x^2+1)/(x^2+2)) end; " }}{PARA 0 "
" 0 "" {TEXT -1 28 "and redo the exercise again." }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 175 "Question: Explain how the following functions  f1
 and  f2 are related by looking at their graphs. You might need to adj
ust the ranges for \"x\" and \"y\" so the graphs look right." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "f1:=proc(x) (x-1)*(x-3)*(x-5
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1(x),x) end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "plot(\{f1(x
),f2(x)\},x=-5..8,y=-20..20,thickness=2); " }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK 
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