View of /trunk/NationalProblemLibrary/ASU-topics/setCalculus/stef/stef4_3p21.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('calculus', 'functions')
    6 ## Tagged by YL
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Single Variable')
   10 ## DBsection('Functions')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('Calculus')
   15 ## EditionText1('5e')
   16 ## AuthorText1('Stewart')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros("PG.pl",
   23            "PGbasicmacros.pl",
   24            "PGchoicemacros.pl",
   25            "PGanswermacros.pl",
   26            "PGauxiliaryFunctions.pl",
   27            "extraAnswerEvaluators.pl");
   28 
   29 $a = random(2,8,1);
   30 $b = random(2,8,1);
   31 
   32 TEXT(beginproblem());
   33 
   34 $showPartialCorrectAnswers = 1;
   35 
   36 TEXT(EV2(<<EOT));
   37 Consider the function
   38 \[ f(x) = \frac{x}{$a x^2 ? {$b}}.  \]
   39 $BR
   40 List the \(x\) values of the inflection points of \(f\).
   41 If there are no inflection points, enter 'NONE'.
   42 $BR
   43  \{ans_rule(30)\}
   44 
   45 EOT
   46 
   47 ANS( number_list_cmp( "0,-sqrt(3*$b/$a),sqrt(3*$b/$a)" , strings=>["none"] ));
   48 
   49 
   50 ENDDOCUMENT();        # This should be the last executable line in the problem.