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    1 ## DESCRIPTION
    2 ##  Calculus: Maximum and Minimum Values
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('derivatives', 'minimum', 'maximum')
    6 ## Tagged by YL
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Applications of Differentiation')
   10 ## DBsection('Maximum and Minimum Values')
   11 ## Date('5/29/2005')
   12 ## Author('Jeff Holt')
   13 ## Institution('UVA')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('4.1')
   18 ## Problem1('37')
   19 
   20 ## TitleText2('Calculus: Early Transcendentals')
   21 ## EditionText2('6')
   22 ## AuthorText2('Stewart')
   23 ## Section2('4.1')
   24 ## Problem2('')
   25 
   26 
   27 DOCUMENT();        # This should be the first executable line in the problem.
   28 
   29 loadMacros(
   30 "PG.pl",
   31 "PGbasicmacros.pl",
   32 "PGchoicemacros.pl",
   33 "PGanswermacros.pl",
   34 "PGauxiliaryFunctions.pl",
   35 "extraAnswerEvaluators.pl"
   36 );
   37 
   38 TEXT(beginproblem());
   39 $showPartialCorrectAnswers = 1;
   40 
   41 $a = random(1,5,1);
   42 $b = random(6,10,1);
   43 $c = random(6,10,1);
   44 $d = sqrt($b*$c)/($b);
   45 
   46 TEXT(EV2(<<EOT));
   47 Find all critical values for the function
   48 \[ f(r) = \frac{$a r}{$b r^2 + $c} \]
   49 and then list them (separated by commas) in the box below.
   50 $PAR
   51 List of critical numbers: \{ans_rule(36) \}
   52 EOT
   53 
   54 $ans = "-$d,$d";
   55 ANS(number_list_cmp($ans));
   56 
   57 ENDDOCUMENT();        # This should be the last executable line in the problem.