View of /trunk/NationalProblemLibrary/Rochester/setVmultivariable7MaxMin/ur_vc_7_2.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 BEGIN_TEXT
   34 Suppose \( f(x, y) = xy - ax - by \).
   35 $PAR
   36 (A) How many local minimum points does \( f \) have in \( \mathbf{R}^{2} \)?  (The
   37 answer is an integer).$BR
   38 \{ ans_rule(5) \}
   39 $PAR
   40 (B) How many local maximum points does \( f \) have in \( \mathbf{R}^{2} \)?$BR
   41 \{ ans_rule(5) \}
   42 $PAR
   43 (C) How many saddle points does \( f \) have in \( \mathbf{R}^{2} \)?$BR
   44 \{ ans_rule(5) \}
   45 END_TEXT
   46 
   47 ANS(num_cmp(0) );
   48 ANS(num_cmp(0) );
   49 ANS(num_cmp(1) );
   50 
   51 
   52 ENDDOCUMENT();    # This should be the last executable line in the problem.