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{SECT 0 {PARA 3 "" 0 "" {TEXT -1 36 "Section 6.3 The Exponential Funct
ion" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "Th
e Maple notation for the exponential function is " }{TEXT 256 4 "exp.
" }{TEXT -1 27 "  Here is an example of its" }}{PARA 0 "" 0 "" {TEXT 
-1 4 "use." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 39 "6.3, Problem 70  is about the function " }{XPPEDIT 18 0 "f(x) =
 (x-3)^2*exp(x);" "6#/-%\"fG6#%\"xG*&),&F'\"\"\"\"\"$!\"\"\"\"#F+-%$ex
pG6#F'F+" }{TEXT -1 9 ".  Graph " }{XPPEDIT 18 0 "f;" "6#%\"fG" }
{TEXT -1 54 " and its first derivative. Comment on the behavior of " }
{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT -1 128 " in relation to the signs \+
and values of its derivative.  Identify significant points on the grap
hs, using calculus as necessary." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 25 "f := x -> (x-3)^2*exp(x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "g := x -> diff(f(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "g(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "pl
ot(\{f(x),g(x)\},x=-2..4);" }}}{PARA 0 "" 0 "" {TEXT -1 13 "The functi
on " }{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT -1 1 " " }{TEXT -1 38 " is i
n red.  (It is only 0 once, when " }{XPPEDIT 18 0 "x = 3.;" "6#/%\"xG$
\"\"$\"\"!" }{TEXT -1 26 ")  The derivative is 0 at " }{XPPEDIT 18 0 "
x = 1;" "6#/%\"xG\"\"\"" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "x = 3;" "
6#/%\"xG\"\"$" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 64 "It is ne
gative between those, which corresponds to the graph of " }{XPPEDIT 
18 0 "f;" "6#%\"fG" }{TEXT -1 34 " decreasing on the interval (1,3)," 
}}{PARA 0 "" 0 "" {TEXT -1 64 "and it is positive elsewhere, which cor
responds to the graph of " }{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT -1 33 
"  incresing elsewhere.  The graph" }}{PARA 0 "" 0 "" {TEXT -1 3 "of \+
" }{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT -1 24 " has a local maximum at \+
" }{XPPEDIT 18 0 "x = 1;" "6#/%\"xG\"\"\"" }{TEXT -1 42 " and a local \+
(in fact, global) minimum at " }{XPPEDIT 18 0 "x = 3;" "6#/%\"xG\"\"$
" }{TEXT -1 20 ".  It has inflection" }}{PARA 0 "" 0 "" {TEXT -1 13 "p
oints where " }{XPPEDIT 18 0 "g;" "6#%\"gG" }{TEXT -1 96 " has a maxim
um or a minimum, in particular, it has one between 2 and 3 and one bet
ween -1 and 0." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diff(g(x),
x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "solve(%=0,x);" }}}
{PARA 0 "" 0 "" {TEXT -1 27 "It is concave down between " }{XPPEDIT 
18 0 "1-sqrt(2);" "6#,&\"\"\"\"\"\"-%%sqrtG6#\"\"#!\"\"" }{TEXT -1 5 "
 and " }{XPPEDIT 18 0 "1+sqrt(2);" "6#,&\"\"\"\"\"\"-%%sqrtG6#\"\"#F%
" }{TEXT -1 15 " and concave up" }{TEXT -1 17 " everywhere else." }}
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