View of /trunk/NationalProblemLibrary/270/setDerivatives13Higher/c2s7p1.pg

    1 ## DESCRIPTION
    2 ## First, second and higher derivatives
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS ('derivatives','second derivative')
    6 ## Tagged by cmd6a 3/8/06
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Differentiation')
   10 ## DBsection('Derivatives of Polynomials and Exponential Functions')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   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 TEXT(beginproblem());
   30 $showPartialCorrectAnswers = 1;
   31 
   32 $a= random(1,10,1);
   33 $b= random(1,2,1);
   34 $c= random(2,5,1);
   35 
   36 TEXT(EV2(<<EOT));
   37 If \( g(t) = ($a -t^{$b})^{$c} \) find
   38 $BR
   39 \(g(0) =\)\{&ans_rule(20) \} $BR
   40 \(g'(0) =\)\{&ans_rule(20) \} $BR
   41 \(g''(0) =\)\{&ans_rule(20) \} $BR
   42 
   43 EOT
   44 
   45 sub tat0 {
   46   my ($power) = @_;
   47   my $out = 0;
   48   $out = 0 if $power > 0;
   49   $out = 1 if $power == 0;
   50   $out = 0 if $power < 0;
   51   $out;
   52   }
   53 
   54 $g0 = ( $a + &tat0($b) )** $c;
   55 $gp0 = $c*($a-&tat0($b) )**($c-1) *(-$b*&tat0($b-1) );
   56 $gp00 = $c*($c-1)*($a-&tat0($b))**($c-2)*($b*$b*&tat0(2*$b-2) )  - $c*($a-&tat0($b))**($c-1)*($b*($b-1)*&tat0($b-2));
   57 
   58 ANS(num_cmp([$g0,$gp0,$gp00], relTol=>.1));
   59 
   60 ENDDOCUMENT();        # This should be the last executable line in the problem.