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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 39 "Finding the slope of a cu
rve at a point" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(stud
ent):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Lets define the function
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e aware that if you want to define a function, you must first define t
he function by stating the independent variable and then an arrow and \+
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-1 39 "Let's take a look at the graph of f(x)." }}}{EXCHG {PARA 0 "> \+
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{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 124 "L
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"" {TEXT -1 38 "Make a preliminary guess at the slope." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }{TEXT -1 145 "Before we guess, let's adjust the wi
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{EXCHG {PARA 0 "" 0 "" {TEXT -1 108 "Let's zoom in at x = 2 and see if
 we can figure out the slope of g(x) at x = 2. Like we did with f(x) a
bove." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "plot(g(x),x=1..3,title=\"g(x)=|x|\");" }}{PARA 13 "" 
1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$7U7$$\"\"\"\"\"!
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$\"1L$ezs$HL>F*$\"1om;/siqmF37$$\"1+]7iI_P>F*$\"13+](y$pZiF37$$\"1nm;_
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\"1LLL*zym1#F*$\"1KLLL*zym'F37$$\"1ML3N1#42#F*$\"1dLL3N1#4(F37$$\"1n;H
Yt7v?F*$\"1im;HYt7vF37$$\"1+++xG**y?F*$\"18+++xG**yF37$$\"1nmT6KU$3#F*
$\"1kmmT6KU$)F37$$\"1LLLbdQ(3#F*$\"1[LLLbdQ()F37$$\"1+]i`1h\"4#F*$\"14
+]i`1h\"*F37$$\"1+]P?Wl&4#F*$\"1F+]P?Wl&*F37$$\"1+++++++@F*F+-%'COLOUR
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1 4 2 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 54 "So what do you think about the slope of g(x) at x = 2?" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "What do y
ou think about the slope of the tangent line to g(x) at x=2?" }}}}
{MARK "27 1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }