View of /trunk/rochester_problib/setDerivatives10MaxMin/s3_1_42.pg

    1 #DESCRIPTION
    2 #KEYWORDS('derivatives', 'critical points', 'minimum,maximum')
    3 #  Find local maximum and minimum of a cubic polynomial
    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(1,5,1);
   20 $b1 = random(6,10,1);
   21 $coef3 = 2;
   22 $coef2 = 3*($a1+$b1);
   23 $coef1 = 6*$a1*$b1;
   24 $coef0 = random(1,11,1);
   25 
   26 TEXT(EV2(<<EOT));
   27 The function \( f(x) = $coef3 x^3 - $coef2 x^2 + $coef1 x + $coef0 \)
   28 has one local minimum and one local maximum. $BR
   29 This function has a local minimum at \( x \) equals \{ans_rule(10) \}
   30 EOT
   31 $ans = $b1;
   32 &ANS(std_num_cmp($ans));
   33 TEXT(EV2(<<EOT));
   34 with value \{ans_rule(20) \} $BR
   35 EOT
   36 $ans = $coef3*$b1**3 - $coef2*$b1**2 + $coef1*$b1 + $coef0;
   37 &ANS(std_num_cmp($ans));
   38 TEXT(EV2(<<EOT));
   39 and a local maximum at \( x \) equals \{ans_rule(10) \}
   40 EOT
   41 $ans = $a1;
   42 &ANS(std_num_cmp($ans));
   43 TEXT(EV2(<<EOT));
   44 with value \{ans_rule(20) \}
   45 EOT
   46 $ans = $coef3*$a1**3 - $coef2*$a1**2 + $coef1*$a1 + $coef0;
   47 &ANS(std_num_cmp($ans));
   48 
   49 ENDDOCUMENT();        # This should be the last executable line in the problem.