View of /trunk/NationalProblemLibrary/ASU-topics/setCalculus/stef/stef4_3p13.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('calculus', 'derivatives')
    6 ## Tagged by YL
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Applications of Differentiation')
   10 ## DBsection('How Derivatives Affect the Shape of a Graph')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('4.3')
   18 ## Problem1('')
   19 
   20 ## TitleText2('Calculus: Early Transcendentals')
   21 ## EditionText2('6')
   22 ## AuthorText2('Stewart')
   23 ## Section2('4.3')
   24 ## Problem2('')
   25 ## TitleText3('Calculus: Early Transcendentals')
   26 ## EditionText3('1')
   27 ## AuthorText3('Rogawski')
   28 ## Section3('4.5')
   29 ## Problem3('79')
   30 
   31 DOCUMENT();        # This should be the first executable line in the problem.
   32 
   33 loadMacros("PG.pl",
   34            "PGbasicmacros.pl",
   35            "PGchoicemacros.pl",
   36            "PGanswermacros.pl",
   37            "PGauxiliaryFunctions.pl",
   38     "extraAnswerEvaluators.pl");
   39 
   40 
   41 $a = random(2,7,1);
   42 $b = random(2,7,1);
   43 $c = random(2,7,1);
   44 
   45 TEXT(beginproblem());
   46 
   47 $showPartialCorrectAnswers = 1;
   48 
   49 TEXT(EV2(<<EOT));
   50 Suppose that
   51 \[ f(x) = \frac{$a x - $b}{x + $c}.  \]
   52 $BR
   53 (A) Find all critical numbers of \(f\).
   54 If there are no critical numbers, enter 'NONE'.
   55 $BR
   56 Critical numbers = \{ans_rule(20)\}
   57 $PAR
   58 EOT
   59 
   60 ANS(str_cmp('NONE'));
   61 
   62 TEXT(EV2(<<EOT));
   63 (B) Use interval notation to indicate where \( f(x) \) is increasing.
   64 $BR
   65 $BBOLD Note: $EBOLD  Use 'INF' for \(\infty\), '-INF' for \(-\infty\),
   66 and use 'U' for the union symbol.
   67 $BR
   68 Increasing: \{ans_rule(35)\}
   69 $PAR
   70 EOT
   71 
   72 @answers = (interval_cmp("(-Inf,-$c)U(-$c,Inf)"));
   73 ANS(@answers );
   74 
   75 TEXT(EV2(<<EOT));
   76 (C) List the \(x\)-coordinates of all local maxima of \(f\).
   77 If there are no local maxima, enter 'NONE'.
   78 $BR
   79 \(x\) values of local maxima = \{ans_rule(20)\}
   80 $PAR
   81 EOT
   82 
   83 ANS(str_cmp('NONE'));
   84 
   85 TEXT(EV2(<<EOT));
   86 (E) List the \(x\)-coordinates of all local minima of \(f\).
   87 If there are no local minima, enter 'NONE'.
   88 $BR
   89  \(x\) values of local minima = \{ans_rule(20)\}
   90 $PAR
   91 EOT
   92 
   93 ANS(str_cmp('NONE'));
   94 
   95 TEXT(EV2(<<EOT));
   96 (F) Use interval notation to indicate where \( f(x) \) is concave up.
   97 $BR
   98 Concave up: \{ans_rule(25)\}
   99 $PAR
  100 EOT
  101 
  102 @answers = (interval_cmp("(-Inf,-$c)"));
  103 ANS(@answers );
  104 
  105 TEXT(EV2(<<EOT));
  106 (G) Use interval notation to indicate where \( f(x) \) is concave down.
  107 $BR
  108 Concave down: \{ans_rule(25)\}
  109 $PAR
  110 EOT
  111 
  112 @answers = (interval_cmp("(-$c,Inf)"));
  113 ANS(@answers );
  114 
  115 TEXT(EV2(<<EOT));
  116 (H) List the \(x\) values of  all inflection points of \(f\).
  117 If there are no inflection points, enter 'NONE'.
  118 $BR
  119 \(x\) values of  inflection points = \{ans_rule(20)\}
  120 $PAR
  121 EOT
  122 
  123 ANS(str_cmp('NONE'));
  124 
  125 TEXT(EV2(<<EOT));
  126 (I) List all horizontal asymptotes of \(f\).
  127  If there are no horizontal asymptotes, enter 'NONE'.
  128 $BR
  129 Horizontal asymptotes \( y = \) \{ans_rule(20)\}
  130 $PAR
  131 EOT
  132 
  133 ANS(number_list_cmp( "$a" , strings=>["none"] ));
  134 
  135 TEXT(EV2(<<EOT));
  136 (J) Find all vertical asymptotes of \(f\).
  137 If there are no vertical asymptotes, enter 'NONE'.
  138 $BR
  139 Vertical asymptotes \( x =\)  \{ans_rule(20)\}
  140 $PAR
  141 EOT
  142 
  143 ANS(number_list_cmp( "-$c" , strings=>["none"] ));
  144 
  145 TEXT(EV2(<<EOT));
  146 (K) Use all of the preceding information to sketch a
  147 graph of \(f\).  When you're finished, enter a "1" in the box
  148 below.
  149 $BR
  150 Graph Complete: \{ans_rule(12)\}
  151 $PAR
  152 EOT
  153 
  154 @answers = (num_cmp(1) );
  155 
  156 ANS(@answers );
  157 
  158 ENDDOCUMENT();        # This should be the last executable line in the problem.