[rochester] / trunk / rochester_problib / setDerivatives10MaxMin / c3s3p2.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

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

Mon Jun 25 19:20:51 2001 UTC (11 years, 11 months ago) by sam
File size: 1105 byte(s)
added problem library as webwork/ww_prob_lib with revision tag prob-lib-2


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