View of /trunk/rochester_problib/setDerivatives10MaxMin/c3s3p2.pg

    1 #DESCRIPTION
    2 #KEYWORDS('maximum,minimum','increasing,decreasing')
    3 # Graphing -- intervals of increase and decrease
    4 # cubic polynomial -
    5 #ENDDESCRIPTION
    6 
    7 DOCUMENT();        # This should be the first executable line in the problem.
    8 
    9 loadMacros("PG.pl",
   10            "PGbasicmacros.pl",
   11            "PGchoicemacros.pl",
   12            "PGanswermacros.pl",
   13 "PGauxiliaryFunctions.pl");
   14 
   15 TEXT(&beginproblem);
   16 $showPartialCorrectAnswers=1;
   17 
   18 $a = random(-8,1,.01); # the two roots of the first derivative
   19 $b = random(1,8,.01);
   20 $c = -6*random(1,3,1);  #
   21 $d = random(-8,8,.01);  # constant term
   22 
   23 $A3=$c/3;
   24 $A2=-$c*($a+$b)/2;
   25 $A1=$c*$a*$b;
   26 $A0 = $d;
   27 
   28 TEXT(EV2(<<EOT));
   29 The  function
   30 \[ f(x) = $A3 x^3 + $A2 x^2 + $A1 x + $A0 \]
   31 is increasing on the interval ( \{ans_rule(5)\} , \{ans_rule(5) \}  ).
   32 $PAR
   33 It is decreasing on the interval ( \(-\infty\), \{ans_rule(5) \} ) and the
   34 interval ( \{ans_rule(5) \}, \(\infty \)  ).
   35 $PAR
   36 The function has a local maximum at \{ans_rule(10) \}.
   37 EOT
   38 
   39 &ANS(std_num_cmp_list(.1, "",$a, $b, $a, $b, $b ));
   40 
   41 ENDDOCUMENT();        # This should be the last executable line in the problem.