View of /trunk/NationalProblemLibrary/ASU-topics/setProductQuotientRule/3-5-09.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Differentiation' 'Product Rule' 'Quotient Rule')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Differentiation')
   10 ## DBsection('The Product and Quotient Rules')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(&beginproblem);
   31 $showpartialcorrectanswers = 1;
   32 
   33 $a = random(2, 13, 1);
   34 $b = random(2,7,1);
   35 $c = random(2,7,1);
   36 $d = random(3,9,1);
   37 $r1 = random(1,12,1);
   38 $r2 = random(-12,-1,1);
   39 
   40 TEXT(EV2(<<EOT));
   41 Let \( f(x) = ($a x^2 + $b x)($c x - $d) \).
   42 Evaluate \( f'(x) \) at the following points:
   43 $BR
   44 (A) \( f'($r1)\) = \{ans_rule(40) \}
   45 $BR
   46 $BR
   47 EOT
   48 
   49 $ans = (2*$a*($r1) + $b)*($c*(($r1)) - $d) + ($a*(($r1)**2) + $b*($r1))*($c);
   50 &ANS(std_num_cmp($ans));
   51 
   52 TEXT(EV2(<<EOT));
   53 (B) \( f'($r2) \) = \{ ans_rule(40) \}
   54 $BR
   55 EOT
   56 
   57 $ans = (2*$a*($r2) + $b)*($c*(($r2)) - $d) + ($a*(($r2)**2) + $b*($r2))*($c);
   58 &ANS(std_num_cmp($ans));
   59 
   60 ENDDOCUMENT();