View of /trunk/rochester_problib/setDerivatives13Higher/s2_7_7.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('derivatives')
    3 ##  Find first and second derivatives of g(s)=(as-b)^c ,
    4 ##  evaluate both at a point
    5 ##ENDDESCRIPTION
    6 
    7 DOCUMENT();        # This should be the first executable line in the problem.
    8 
    9 loadMacros(
   10 "PG.pl",
   11 "PGbasicmacros.pl",
   12 "PGchoicemacros.pl",
   13 "PGanswermacros.pl",
   14 "PGauxiliaryFunctions.pl"
   15 );
   16 
   17 TEXT(&beginproblem);
   18 $showPartialCorrectAnswers = 1;
   19 
   20 $a1 = random(2,5,1);
   21 $b1 = random(1,8,1);
   22 $c1 = random(6,9,1);
   23 $x1 = random(1,5,1);
   24 $c2=$c1-1;
   25 $c3=$c2-1;
   26 $deriv1f = "$c1 * ($a1*s -$b1)^$c2 * $a1";
   27 $deriv1 = $c1 * ($a1*$x1 -$b1)**($c1-1) * $a1;
   28 $deriv2f = "$c1*$c2*($a1*s -$b1)^$c3 * $a1^2";
   29 $deriv2 = $c1*$c2*($a1*$x1 -$b1)**$c3 * $a1*$a1;
   30 
   31 TEXT(EV2(<<EOT));
   32 Let \( g(s) = ( $a1 s - $b1)^ $c1   \). $BR
   33 Then \( g'(s) \) is \{ans_rule(30) \} $BR
   34 \( g'( $x1 ) \) is \{ans_rule(30) \}, $BR
   35 EOT
   36 
   37 $ans1 = $deriv1f;
   38 $ans2 = $deriv1;
   39 &ANS(function_cmp($ans1, "s"));
   40 &ANS(std_num_cmp($ans2));
   41 TEXT(EV2(<<EOT));
   42 \( g''(s) \) is \{ans_rule(30) \} $BR
   43 and \( g''( $x1 ) \) is \{ans_rule(30) \}
   44 EOT
   45 
   46 $ans3 = $deriv2f;
   47 $ans4 = $deriv2;
   48 &ANS(function_cmp($ans3, "s"));
   49 &ANS(std_num_cmp($ans4));
   50 ENDDOCUMENT();        # This should be the last executable line in the problem.