[rochester] / trunk / rochester_problib / setDerivatives1_5Tangents / ur_dr_1_5_4.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

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

Mon Jun 25 19:20:51 2001 UTC (11 years, 11 months ago) by sam
File size: 1305 byte(s)
added problem library as webwork/ww_prob_lib with revision tag prob-lib-2


    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
10 "PG.pl",
11 "PGbasicmacros.pl",
12 "PGchoicemacros.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.