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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('55')
   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("PG.pl",
   30            "PGbasicmacros.pl",
   31            "PGchoicemacros.pl",
   32            "PGanswermacros.pl",
   33            "PGauxiliaryFunctions.pl");
   34 
   35 $a = random(2,8,2);
   36 $p1 = random(1/2,3,1/2);
   37 $p2 = random(4,6,1);
   38 
   39 TEXT(beginproblem());
   40 
   41 $showPartialCorrectAnswers = 1;
   42 
   43 TEXT(EV2(<<EOT));
   44 Find the
   45 absolute maximum and absolute minimum values of  the function
   46 \[  f(x) = x^$a + \frac{$a}{x}   \]
   47 on the interval \([$p1,$p2]\).
   48 $BR
   49 Enter -1000 for any absolute extrema that does not exist.
   50 $BR
   51 Absolute maximum = \{ans_rule(20)\}
   52 $BR
   53 $BR
   54 Absolute minimum = \{ans_rule(20)\}
   55 
   56 $BR
   57 EOT
   58 
   59 $ans1 = (1)**$a +$a/(1);
   60 $ans2 = ($p1)**$a +$a/($p1);
   61 $ans3 = ($p2)**$a +$a/($p2);
   62 
   63 if ($p1 < 1) {
   64     $ansmin = $ans1;
   65 }
   66 else {
   67     $ansmin = $ans2;
   68 }
   69 
   70 $ansmax = $ans3;
   71 
   72 @answers = (num_cmp($ansmax), num_cmp($ansmin));
   73 
   74 ANS(@answers);
   75 
   76 ENDDOCUMENT();        # This should be the last executable line in the problem.