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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 66 "MAT 155                 Project X                        Fall 2
002" }}{PARA 0 "" 0 "" {TEXT -1 91 "                   Concavity and I
nflection                                                " }{MPLTEXT 
1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 1 " " }{MPLTEXT 1 0 0 "" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 126 "Your work should be done neatly in the \+
same format as previous labs and saved regularly as yourname10.mws and
 yourname10b.mws." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 256 38 "You should write comments as you work." }{TEXT -1 199 " \+
 To do so just backspace in front of the prompt > and type in the comm
ents.  They should appear in black not in red.   When you finish the l
ab be sure to go over your comments and check the grammar." }}}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 73 "Problem 1: a)  Define the function g(x)=x^3-2x and graph \+
it from -5 to 5." }}{PARA 0 "" 0 "" {TEXT -1 76 "Approximately where i
s it increasing?  Approximately where is it decreasing?" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 71 "b)  Find its derivat
ive using D(g).  Graph the derivative from -5 to 5." }}{PARA 0 "" 0 "
" {TEXT -1 65 "Use fsolve to find out exactly where it switches from p
ositive to" }}{PARA 0 "" 0 "" {TEXT -1 42 "negative.  Graph D(g) and g
 together using" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "plot(\{D(g)(x), \+
g(x)\}, x=-5..5);" }}{PARA 0 "" 0 "" {TEXT -1 48 "Exactly where is g(x
) increasing and decreasing?" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}
{PARA 0 "" 0 "" {TEXT -1 72 "c)  Now find D(D(g)) and plot it with g. \+
 What is the sign of D(D(g)) at" }}{PARA 0 "" 0 "" {TEXT -1 66 "x wher
e g has a local maximum? local minimum?  Is g curving upward" }}{PARA 
0 "" 0 "" {TEXT -1 69 "(concave up) when its second derivative is posi
tive?  What about when" }}{PARA 0 "" 0 "" {TEXT -1 34 "the second deri
vative is negative?" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "
" {TEXT -1 73 "Problem 2:  Repeat problem 1 for f(x)=sin(x) focusing o
n x= -2Pi to 2Pi.." }{MPLTEXT 1 0 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 " \+
" }{MPLTEXT 1 0 0 "" }}{PARA 0 "" 0 "" {TEXT -1 71 "Problem 3:  Repeat
 problem 1 for f(x)=(x^2-1)/x focusing on x= -3 .. 3." }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 40 "Exploration:  Try some
 other functions. " }}}}{MARK "5" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 
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