View of /trunk/rochester_problib/setDerivatives13Higher/s2_7_4.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('derivatives')
    3 ##  Find first and second derivatives of a polynomial, evaluate both at a point
    4 ##ENDDESCRIPTION
    5 
    6 DOCUMENT();        # This should be the first executable line in the problem.
    7 
    8 loadMacros(
    9 "PG.pl",
   10 "PGbasicmacros.pl",
   11 "PGchoicemacros.pl",
   12 "PGanswermacros.pl",
   13 "PGauxiliaryFunctions.pl"
   14 );
   15 
   16 TEXT(&beginproblem);
   17 $showPartialCorrectAnswers = 1;
   18 
   19 $a1 = random(2,5,1);
   20 $b1 = random(2,8,1);
   21 $c1 = random(2,4,1);
   22 $d1 = random(1,10,1);
   23 $x1 = random(1,5,1);
   24 $deriv1f = "7*x^6 - 5*$a1*x^4 +3*$b1*x^2 - $c1";
   25 $deriv1 = 7*$x1**6 - 5*$a1*$x1**4 +3*$b1*$x1**2 - $c1;
   26 $deriv2f = "42*x^5 - 20*$a1*x^3 +6*$b1*x";
   27 $deriv2 = 42*$x1**5 - 20*$a1*$x1**3 +6*$b1*$x1;
   28 
   29 TEXT(EV2(<<EOT));
   30 Let \( f(x) = x^7- $a1 x^5 + $b1 x^3 - $c1 x - $d1  \). $BR
   31 Then \( f'(x) \) is \{ans_rule(30) \} $BR
   32 \( f'( $x1 ) \) is \{ans_rule(30) \} $BR
   33 EOT
   34 
   35 $ans1 = $deriv1f;
   36 $ans2 = $deriv1;
   37 &ANS(function_cmp($ans1));
   38 &ANS(std_num_cmp($ans2));
   39 TEXT(EV2(<<EOT));
   40 \( f''(x) \) is \{ans_rule(30) \} $BR
   41 and \( f''( $x1 ) \) is \{ans_rule(30) \}
   42 EOT
   43 
   44 $ans3 = $deriv2f;
   45 $ans4 = $deriv2;
   46 &ANS(function_cmp($ans3));
   47 &ANS(std_num_cmp($ans4));
   48 ENDDOCUMENT();        # This should be the last executable line in the problem.