View of /branches/UGA/5.2.3.pg

    1 ## DESCRIPTION
    2 ##   Locate Critical Points
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Critical', 'Point', 'Partial', 'Multivariable')
    6 ## Tagged by nhamblet
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Partial Derivatives')
   10 ## DBsection('Maximum and Minimum Values')
   11 ## Date('October 29, 2009')
   12 ## Author('Shifrin')
   13 ## Institution('UGA')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23   "PGstandard.pl",
   24   "PGunion.pl",
   25   "Parser.pl",
   26   "parserVectorUtils.pl",
   27   "PGcourse.pl"
   28 );
   29 
   30 
   31 TEXT(beginproblem());
   32 BEGIN_PROBLEM();
   33 
   34 ##############################################
   35 #  Setup
   36 
   37 Context("Vector");
   38 
   39 #
   40 #  The function
   41 #
   42 do{$c = non_zero_random(-5,5,1)} until ($c**2 != 1);
   43 $a = $c**2 - 1;
   44 $b = 3*$c**2;
   45 
   46 
   47 
   48 $f = Formula("x^3 + 3*$a x y^2 - 3*$a y^2 - $b x")->reduce;
   49 $arg = '\left(\begin{array}{c} x\\y \end{array}\right)';
   50 
   51 
   52 #
   53 #  Critical points
   54 #
   55 $P1 = Point($c,0);
   56 $P2 = Point(-$c,0);
   57 $P3 = Point(1,1);
   58 $P4 = Point(1,-1);
   59 
   60 ##############################################
   61 #  Main text
   62 
   63 Context()->texStrings;
   64 BEGIN_TEXT
   65 
   66 Find all the critical points of the function \(f $arg=$f\).
   67 
   68 $PAR
   69 List the points using ordered pair notation \( (a,b) \), separated by commas.
   70 $PAR
   71 
   72 $BCENTER
   73 \{ans_rule(50)\}
   74 $ECENTER
   75 
   76 
   77 
   78 END_TEXT
   79 Context()->normalStrings;
   80 
   81 ##################################################
   82 #  Answers
   83 
   84 ANS(List($P1,$P2,$P3,$P4)->cmp);
   85 
   86 $showPartialCorrectAnswers = 1;
   87 
   88 ##################################################
   89 
   90 END_PROBLEM();
   91 ENDDOCUMENT();        # This should be the last executable line in the problem.