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`Moving UMN contributions to NPL`

```    1 #DESCRIPTION
2 ##  Calculus: Derivatives
3 ##ENDDESCRIPTION
4
5 ##KEYWORDS('calculus', 'derivative', 'graph')
6
7 ## DBsubject('Calculus')
8 ## DBchapter('Limits and Derivatives')
9 ## DBsection('The Derivative as a Function')
10 ## Date('09/27/2010')
11 ## Author('Justin Sukiennik')
12 ## Institution('University of Minnesota')
13 ## TitleText1('Calculus: Concepts and Contexts')
14 ## EditionText1('4 Custom UMTYMP Ed.')
15 ## AuthorText1('Stewart')
16 ## Section1('2.8')
17 ## Problem1('3')
18
19 #####################################################################
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23   "PGstandard.pl",
24   "PGunion.pl",            # Union College utilities
25   "MathObjects.pl",
26   "PGgraphmacros.pl",
27   "PGcourse.pl",
28 );
29 #####################################################################
30
31 TEXT(beginproblem());
32
34
36
37 #####################################################################
38
39 Context("Numeric");
40
41 # Let students type "EmptySet" instead of "NONE"
43 Context()->flags->set(noneWord=>"EmptySet");
44
45 \$c = random(3,4,1);
46
47 if (\$c==4){
48 \$d = Compute("0.054");
49 }
50 else{
51 \$d = Compute("0.12");
52 }
53
54 \$a = random(-4,-3,1);
55 \$b = random(-2,-1,1);
56
57 Context("Interval");
58
59 # Let students type "EmptySet" instead of "NONE"
61 Context()->flags->set(noneWord=>"EmptySet");
62
63 \$an1 = Interval("(-infinity,\$a)");
64 \$an2 = Interval("(\$b,0)");
65 \$an3 = Interval("(\$c, infinity)");
66
67 \$an4 = Interval("(\$a, \$b)");
68 \$an5 = Interval("(0,\$c)");
69
70 \$ans1 = Union("\$an1 U \$an2 U \$an3");
71 \$ans2 = Union("\$an4 U \$an5");
72
73 ###############################################################
74
75 \$w = 400;  # graph size
76 \$tw = 500; # graph size in TeX
77
78 \$graph1 = init_graph(-6,-6,6,6,'axes'=>[0,0],'ticks'=>[12,12],'grid'=>[12,12],'size'=>[500,500]);
79
80 \$p1 = FEQ("(\$d)*x(x-\$a)(x-\$b)(x-\$c) for x in <-6,-3> using color:blue weight:2");
81 \$p2 = FEQ("(\$d)*x(x-\$a)(x-\$b)(x-\$c) for x in <-3,3> using color:blue weight:2");
82 \$p3 = FEQ("(\$d)*x(x-\$a)(x-\$b)(x-\$c) for x in <3,6> using color:blue weight:2");
83
84 plot_functions(\$graph1,\$p1,\$p2,\$p3);
85
86 #Title("\$BITALIC Look Ahead: \$EITALIC 2.8 What Does f' Say About f?");
87
88 ###############################################################
89 Context()->texStrings;
90
91 BEGIN_TEXT
92 The given graph of the \$BITALIC derivative \$EITALIC \(f'\) of a function \(f\) is shown.  Assuming  the graphs continue in the same way as \(x\) goes to infinity and negative infinity, answer the following questions.
93 \$PAR
94 \$BCENTER
95 \{image(insertGraph(\$graph1),width=>\$w,height=>\$w,tex_size=>\$tw)\}
96 \$ECENTER
97 \$HR
98 \$BBOLD 1. \$EBOLD On what intervals is \(f\) increasing? \$BR
99 Answer (in interval notation): \{ans_rule(30)\} \$PAR
100 \$BBOLD 2. \$EBOLD On what intervals is \(f\) decreasing? \$BR
101 Answer (in interval notation): \{ans_rule(30)\} \$PAR
102 \$HR
103 \$BBOLD Note: \$EBOLD \$BITALIC You can click on the graph to enlarge the image.\$EITALIC
104 \$HR
105 END_TEXT
106
107 Context()->normalStrings;
108
109 #####################################################################
110
111 ANS( \$ans1->cmp );
112 ANS( \$ans2->cmp );
113
114 ENDDOCUMENT();        # This should be the last executable line in the problem.
```