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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 39 "Understanding max/min/inf
lection 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:=proc(x) diff(g(x),x) end;" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 15 "simplify(h(x));" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 66 "Exercise: (1) Can you determine which one is f, g, h resp
ectively?" }}{PARA 0 "" 0 "" {TEXT -1 85 "(2) What is the relationship
 between max/min of  f ' and the inflection points of  f." }}{PARA 0 "
" 0 "" {TEXT -1 106 "(3) Find the inflection points of  f. Can you exp
lain how the inflection points are related to f'' (or h)?" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plot(\{f(x),g(x),h(x)\},x=-5..5,thi
ckness=2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 70 "Exercise: Use the function  f:=proc(x) ar
ccot((2*x^2+1)/(x^2+2)) end; " }}{PARA 0 "" 0 "" {TEXT -1 28 "and redo
 the exercise again." }}}}{MARK "11" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 
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