View of /trunk/NationalProblemLibrary/ASU-topics/setFirstDerivative/4-2-29.pg

    1 ## DESCRIPTION
    2 ## Information from the First Derivative
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('calculus', 'first derivative', 'critical points', 'minimum', 'maximum', 'increasing', 'decreasing')
    6 ## Tagged by XW
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Applications of Differentiation')
   10 ## DBsection('How Derivatives Affect the Shape of a Graph')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('4.3')
   18 ## Problem1('')
   19 
   20 ## TitleText2('Calculus: Early Transcendentals')
   21 ## EditionText2('6')
   22 ## AuthorText2('Stewart')
   23 ## Section2('4.3')
   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     "extraAnswerEvaluators.pl");
   35 
   36 
   37 $a = random(2,9,2);
   38 $b = non_zero_random(-9,9,2);
   39 
   40 TEXT(beginproblem());
   41 
   42 $showPartialCorrectAnswers = 1;
   43 
   44 
   45 
   46 TEXT(EV2(<<EOT));
   47 Let
   48 \[ f(x) = $a x^3 ? {$b}.  \]
   49 $BR
   50 (A) Use interval notation to indicate where \( f(x) \) is increasing.
   51 $PAR
   52 $PAR
   53 $BBOLD Note:$EBOLD When using interval notation in WeBWorK, remember
   54 that:
   55 $BR
   56 (i) You use 'I' for \(\infty\) and '-I' for \(-\infty\).$BR
   57 (ii) 'U' for the union symbol.$BR
   58 (iii) If the interval is empty, write "{}" without the quotation marks.$BR
   59 $BR
   60 
   61 Increasing: \{ans_rule(25)\}
   62 $PAR
   63 $PAR
   64 EOT
   65 
   66 @answers = (interval_cmp("(-I,I)"));
   67 
   68 ANS(@answers );
   69 
   70 TEXT(EV2(<<EOT));
   71 $BR
   72 (B) Use interval notation to indicate where \( f(x) \) is decreasing.
   73 $PAR
   74 Decreasing: \{ans_rule(25)\}
   75 $PAR
   76 $PAR
   77 EOT
   78 
   79 @answers = (str_cmp("{}") );
   80 
   81 ANS(@answers );
   82 
   83 TEXT(EV2(<<EOT));
   84 $BR
   85 (C) Find the average of the \(x\) values of all local maxima of
   86 \(f\).
   87 $BR
   88 Note: If there are no local maxima, enter -1000.
   89 $PAR
   90 Average of \(x\) values = \{ans_rule(7)\}
   91 $PAR
   92 $PAR
   93 EOT
   94 
   95 @answers = (num_cmp(-1000) );
   96 
   97 ANS(@answers );
   98 
   99 TEXT(EV2(<<EOT));
  100 $BR
  101 (D) Find the average of the \(x\) values of all local minima of
  102 \(f\).
  103 $BR
  104 Note: If there are no local minima, enter -1000.
  105 $PAR
  106 Average of \(x\) values = \{ans_rule(7)\}
  107 $PAR
  108 $PAR
  109 EOT
  110 
  111 @answers = (num_cmp(-1000) );
  112 
  113 ANS(@answers );
  114 
  115 ENDDOCUMENT();        # This should be the last executable line in the problem.