View of /trunk/NationalProblemLibrary/Rochester/setVmultivariable7MaxMin/ur_vc_7_13.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('critical points' 'minimum' 'maximum' 'multivariable')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Partial Derivatives')
   10 ## DBsection('Maximum and Minimum Values')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 
   21 DOCUMENT();   # This should be the first executable line in the problem.
   22 
   23 loadMacros("PG.pl",
   24            "PGbasicmacros.pl",
   25            "PGchoicemacros.pl",
   26            "PGanswermacros.pl",
   27            "PGauxiliaryFunctions.pl"
   28           );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a = random(2, 9, 1);
   34 $b = random(2, 9, 1);
   35 
   36 BEGIN_TEXT
   37 Find the maximum and minimum values of  \( f(x, y) = xy \) on the ellipse
   38 \( $a\!x^{2} + y^{2} = $b \).
   39 $BR
   40 maximum value = \{ ans_rule(20) \}$BR
   41 minimum value = \{ ans_rule(20) \}
   42 END_TEXT
   43 
   44 ANS(num_cmp( .5*$b/sqrt($a) ) );
   45 ANS(num_cmp( - .5*$b/sqrt($a) ) );
   46 
   47 ENDDOCUMENT();    # This should be the last executable line in the problem.