View of /trunk/rochester_problib/instructiveProblems/NewProblems/osu_dr_10_1N.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('exponentials', 'increase,decrease', 'concavity')
    3 ##Ellis & Gulick section 6.2 #12
    4 ##Authored by Zig Fiedorowicz 1/17/2000
    5 ##ENDDESCRIPTION
    6 
    7 DOCUMENT();
    8 
    9 loadMacros(
   10 "PGstandard.pl",
   11 "MathObjects.pl",
   12 "PGcourse.pl",
   13 # "source.pl",
   14 );
   15 
   16 TEXT(beginproblem());
   17 $showPartialCorrectAnswers = 1;
   18 
   19 ###################
   20 #
   21 #  Setup
   22 
   23 Context("Interval");
   24 
   25 Context()->strings->add(NA=>{},"Not Applicable"=>{alias=>'NA'},
   26      "none"=>{alias=>'NA'});
   27 
   28 # This adds the string "NA" as an acceptable String to be used and entered as
   29 #    an answer, and makes the strings "Not Applicable" and "none" act as "NA"
   30 #    (i.e. if "NA" is correct and the student enters "Not Applicable" - s/he
   31 #    will receive correct).  This is useful if the student is supposed to either
   32 #    enter a value or potentially some string, to avoid giving the student an
   33 #    error message if the answer checker is expecting a number and it receives
   34 #    the string "NA".
   35 
   36 $aa = random(1,10,1);
   37 
   38 $Funct  = Formula("e^x/($aa + e^x)")->reduce;
   39 $Deriv  = $Funct->D->reduce;
   40 $Deriv2 = $Deriv->D->reduce;
   41 
   42 $Interv1 = Interval("(-INF,INF)"); # Represents: (-∞,∞)
   43 $Interv2 = String("NA");
   44 
   45 $Interv3 = Interval("(-INF,log($aa))");
   46 $Interv4 = Interval("(log($aa),INF)");
   47 
   48 $InfPt = Real("log($aa)");
   49 
   50 ###################
   51 #
   52 #  Text
   53 
   54 Context()->texStrings;
   55 BEGIN_TEXT
   56 Consider the function
   57 \[f(x)= $Funct\]
   58 $PAR
   59 Then \(f'(x)\)  =  \{ ans_rule()\}
   60 $BR
   61 
   62 The following questions ask for endpoints of intervals of
   63 increase or decrease for the function \(f(x)\). $BR  Write INF
   64 for \(\infty\), -INF for \(-\infty\), and NA (ie. not applicable) if
   65 there are no intervals of that type.
   66 $PAR
   67 The interval of increase for \(f(x)\) is: \{ ans_rule()\}
   68 $PAR
   69 The interval of decrease for \(f(x)\) is: \{ ans_rule()\}
   70 $PAR
   71 \(f(x)\) has a local minimum at \{ ans_rule()\}. (Put NA if none.)
   72 $BR
   73 
   74 \(f(x)\) has a local maximum at \{ ans_rule()\}. (Put NA if none.)
   75 $BR
   76 
   77 Then \(f''(x)\)  =  \{ ans_rule(40)\}
   78 $BR
   79 
   80 The following questions ask for intervals of
   81 upward and downward concavity for the function \(f(x)\).  $BR Type INF
   82 for \(\infty\), -INF for \(-\infty\), and put NA if
   83 there are no intervals of that type.
   84 $PAR
   85 
   86 The interval of upward concavity for \(f(x)\) is: \{ ans_rule()\}
   87 $PAR
   88 The interval of downward concavity for \(f(x)\) is: \{ ans_rule()\}
   89 $PAR
   90 \(f(x)\) has a point of inflection at \{ ans_rule()\}. (Put NA if none.)
   91 
   92 END_TEXT
   93 Context()->normalStrings;
   94 
   95 ###################
   96 #
   97 #  Textbook Reference:
   98 
   99 ##set $PG_environment{'textbook'} in webworkCourse.ph
  100 if (defined($textbook)) {
  101    if ($textbook eq "EllisGulick5") {
  102 BEGIN_TEXT
  103 $PAR
  104 This is similar to problem 12 of Section 6.2 of the text.
  105 END_TEXT
  106 }
  107 }
  108 
  109 ###################
  110 #
  111 #  Answers
  112 
  113 ANS($Deriv->cmp);
  114 ANS($Interv1->cmp(typeMatch=>Value::Interval,
  115    showEndpointHints => 0, showEndTypeHints => 0));
  116 ANS($Interv2->cmp(typeMatch=>Value::Interval,
  117    showEndpointHints => 0, showEndTypeHints => 0));
  118    # This is needed because the default for the interval answer checker is to
  119    #    return a response as to whether both, one or neither of your endpoints
  120    #    are correct, but does not do this if the answer checker is expecting a
  121    #    string or a union of intervals.  Thus to avoid ambiguity and confusion,
  122    #    these messages are turned off.
  123 
  124 ANS(String("NA")->cmp);
  125 ANS(String("NA")->cmp);
  126 ANS($Deriv2->cmp);
  127 ANS($Interv3->cmp(typeMatch=>Value::Interval,
  128    showEndpointHints => 0, showEndTypeHints => 0));
  129 ANS($Interv4->cmp(typeMatch=>Value::Interval,
  130    showEndpointHints => 0, showEndTypeHints => 0));
  131 ANS($InfPt->cmp);
  132 
  133 ENDDOCUMENT();