View of /trunk/rochester_problib/setDerivatives1_5Tangents/ur_dr_1_5_4.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('derivatives', 'tangent line')
    3 ##  Find the derivatives of a polynomial evaluated at a point, use that to
    4 ##  find the equation of the tangent line of the curve at that 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(2,3,1);
   22 $c1 = random(2,7,1);
   23 $d1 = random(2,6,1);
   24 $n1 = random(3,7,1);
   25 $x1 = random(4,5,1);
   26 $y1 = $a1*$x1+$b1/$x1;
   27 $m1 = $a1-$b1*$x1**(-2);
   28 
   29 TEXT(EV2(<<EOT));
   30 If \( f(x) = $a1 x + \frac{ $b1 }{x} \), find \( f'( $x1 ) \).
   31 $BR $BR \{ans_rule(20) \}
   32 $BR
   33 EOT
   34 
   35 $ans = $m1;
   36 &ANS(std_num_cmp($ans));
   37 
   38 TEXT(EV2(<<EOT));
   39 Use this to find the equation of the tangent line to the curve
   40  \( y =   $a1 x + \frac{ $b1 }{x} \)
   41 at the point \( ( $x1 , !{$y1:%.5f} ) \).
   42 The equation of this tangent line can be written in the form \( y = mx+b \)
   43 where \( m \) is: \{ans_rule(20) \}
   44 $BR
   45 EOT
   46 $ans = $m1;
   47 &ANS(std_num_cmp($ans));
   48 
   49 TEXT(EV2(<<EOT));
   50 and  where \( b \) is: \{ans_rule(20) \}
   51 $BR
   52 EOT
   53 $ans = $y1 -$m1*$x1;
   54 &ANS(std_num_cmp($ans));
   55 
   56 ENDDOCUMENT();        # This should be the last executable line in the problem.