View of /trunk/NationalProblemLibrary/UMN/calculusStewartCCC/s_2_8_3.pg

    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 
   22 loadMacros(
   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 
   33 install_problem_grader(~~&std_problem_grader);
   34 
   35 $showPartialCorrectAnswers = 0;
   36 
   37 #####################################################################
   38 
   39 Context("Numeric");
   40 
   41 # Let students type "EmptySet" instead of "NONE"
   42 Context()->constants->add(EmptySet => Set());
   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"
   60 Context()->constants->add(EmptySet => Set());
   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.