View of /trunk/rochester_problib/setDerivatives1_5Tangents/ur_dr_1_5_3.pg

    1 ##DESCRIPTION
    2 ##  Find the equation of a tangent line at a point by finding its derivative
    3 ##  at that point
    4 ##ENDDESCRIPTION
    5 
    6 ##KEYWORDS('tangent line', 'derivatives')
    7 
    8 DOCUMENT();        # This should be the first executable line in the problem.
    9 
   10 loadMacros(
   11 "PG.pl",
   12 "PGbasicmacros.pl",
   13 "PGchoicemacros.pl",
   14 "PGanswermacros.pl",
   15 "PGauxiliaryFunctions.pl"
   16 );
   17 
   18 TEXT(&beginproblem);
   19 $showPartialCorrectAnswers = 1;
   20 
   21 $a1 = random(1,8,1);
   22 
   23 $x1=0;
   24 while ($x1==0) {
   25     $x1 = random(-5,5,1);
   26 }
   27 $y1 = $a1/$x1;
   28 $m1 = -$a1/$x1**2;
   29 
   30 TEXT(EV2(<<EOT));
   31 If \( f(x) = \frac{$a1}{x} \), find \( f'( $x1 ) \).
   32 \{ ans_rule(20) \}
   33 $BR
   34 EOT
   35 
   36 $ans = $m1;
   37 &ANS(std_num_cmp($ans));
   38 
   39 TEXT(EV2(<<EOT));
   40 Use this to find the equation of the tangent line to the hyperbola
   41  \( y = \frac{$a1}{x} \)
   42 at the point \( ( $x1 , {$y1:%0.3f} ) \).
   43 The equation of this tangent line can be written in the form \( y = mx+b \)
   44 where \( m \) is:\{ans_rule(20)  \}
   45 $BR
   46 EOT
   47 $ans = $m1;
   48 &ANS(std_num_cmp($ans));
   49 
   50 TEXT(EV2(<<EOT));
   51 and  where \( b \) is:
   52 \{ans_rule(20)  \}
   53 $BR
   54 EOT
   55 $ans = $y1 -$m1*$x1;
   56 &ANS(std_num_cmp($ans));
   57 
   58 ENDDOCUMENT();        # This should be the last executable line in the problem.