Merge pull request #1437 from dlglin/update-ASU-max-min

Convert problem to PGML

Author: dlglin

OpenProblemLibrary/ASU-topics/setOptimization/4-5-23.pg

@@ -11,119 +11,64 @@
 ## Level(4)
 ## KEYWORDS('Optimization' 'Maximum' 'Minimum')
 
-DOCUMENT();        # This should be the first executable line in the problem.
+DOCUMENT();    # This should be the first executable line in the problem.
 
-loadMacros(
-  "PGstandard.pl",
-  "PGchoicemacros.pl",
-  "PGcourse.pl"
-);
+loadMacros('PGstandard.pl', 'PGML.pl', 'PGcourse.pl');
 
-$at = non_zero_random(-4,4,2);
-$a = $at + 5;
-$b = 10-$a;
-$c0 = random(2,12,1);
-$c1 = -3*$a*$b;
-$c2 = 3*($b-$a)/2;
-$p1 = -$b -1;
+$at = non_zero_random(-4, 4, 2);
+$a  = $at + 5;
+$b  = 10 - $a;
+$c0 = random(2, 12, 1);
+$c1 = -3 * $a * $b;
+$c2 = 3 * ($b - $a) / 2;
+$p1 = -$b - 1;
 $p2 = -$b + 2;
 $p3 = $a - 1;
 $p4 = $a + 1;
 
+$f = Formula("x^3+$c2*x^2+$c1*x+$c0")->reduce();
 
-TEXT(beginproblem());
-
-$showPartialCorrectAnswers = 1;
-
-TEXT(EV2(<<EOT));
-Find the
-absolute maximum and absolute minimum values of  the function
-\[  f(x) = x^3 ? {$c2} x^2 ? {$c1} x + $c0 \]
-on each of the indicated intervals.
-$BR
-Enter -1000 for any absolute extrema that does not exist.
-$BR
-$BR
-(A) Interval = \([$p1, 0]\).
-$BR
-Absolute maximum = \{ans_rule(10)\}
-$BR
-$BR
-Absolute minimum = \{ans_rule(10)\}
-
-$BR
-EOT
-
-$ans1 = -($b**3) + $c2*$b**2 - $c1*$b + $c0;
-if ($p1**3 + $c2*$p1**2 + $c1*$p1 < 0)
-{
-    $ans2 = $p1**3 + $c2*$p1**2 + $c1*$p1 + $c0;
-}
-else
-{
+$ans1 = -($b**3) + $c2 * $b**2 - $c1 * $b + $c0;
+if ($p1**3 + $c2 * $p1**2 + $c1 * $p1 < 0) {
+    $ans2 = $p1**3 + $c2 * $p1**2 + $c1 * $p1 + $c0;
+} else {
     $ans2 = $c0;
 }
-@answers = (num_cmp($ans1), num_cmp($ans2));
-
-ANS(@answers);
-
-TEXT(EV2(<<EOT));
-$BR
-(B) Interval = \([$p2, $p4]\).
-$BR
-Absolute maximum = \{ans_rule(10)\}
-$BR
-$BR
-Absolute minimum = \{ans_rule(10)\}
-
-$BR
-EOT
 
-if ($p2**3 + $c2*$p2**2 + $c1*$p2 < $p4**3 + $c2*$p4**2 + $c1*$p4)
-{
-    $ans1 = $p4**3 + $c2*$p4**2 + $c1*$p4 + $c0;
+if ($p2**3 + $c2 * $p2**2 + $c1 * $p2 < $p4**3 + $c2 * $p4**2 + $c1 * $p4) {
+    $ans3 = $p4**3 + $c2 * $p4**2 + $c1 * $p4 + $c0;
+} else {
+    $ans3 = $p2**3 + $c2 * $p2**2 + $c1 * $p2 + $c0;
 }
-else
-{
-    $ans1 = $p2**3 + $c2*$p2**2 + $c1*$p2 + $c0;
-}
-$ans2 = ($a**3) + $c2*$a**2 + $c1*$a + $c0;
-
-@answers = (num_cmp($ans1), num_cmp($ans2));
-
-ANS(@answers);
-
-TEXT(EV2(<<EOT));
-$BR
-(C) Interval = \([$p1, $p4]\).
-$BR
-Absolute maximum = \{ans_rule(10)\}
-$BR
-$BR
-Absolute minimum = \{ans_rule(10)\}
+$ans4 = ($a**3) + $c2 * $a**2 + $c1 * $a + $c0;
 
-$BR
-EOT
-
-if ($p4**3 + $c2*$p4**2 + $c1*$p4 < (-$b)**3 + $c2*$b**2 - $c1*$b)
-{
-    $ans1 = (-$b)**3 + $c2*$b**2 - $c1*$b + $c0;
-}
-else
-{
-    $ans1 = $p4**3 + $c2*$p4**2 + $c1*$p4 + $c0;
+if ($p4**3 + $c2 * $p4**2 + $c1 * $p4 < (-$b)**3 + $c2 * $b**2 - $c1 * $b) {
+    $ans5 = (-$b)**3 + $c2 * $b**2 - $c1 * $b + $c0;
+} else {
+    $ans5 = $p4**3 + $c2 * $p4**2 + $c1 * $p4 + $c0;
 }
-if ($p1**3 + $c2*$p1**2 + $c1*$p1 > ($a)**3 + $c2*$a**2 + $c1*$a)
-{
-    $ans2 = ($a)**3 + $c2*$a**2 + $c1*$a + $c0;
-}
-else
-{
-    $ans2 = $p1**3 + $c2*$p1**2 + $c1*$p1 + $c0;
+if ($p1**3 + $c2 * $p1**2 + $c1 * $p1 > ($a)**3 + $c2 * $a**2 + $c1 * $a) {
+    $ans6 = ($a)**3 + $c2 * $a**2 + $c1 * $a + $c0;
+} else {
+    $ans6 = $p1**3 + $c2 * $p1**2 + $c1 * $p1 + $c0;
 }
 
-@answers = (num_cmp($ans1), num_cmp($ans2));
+BEGIN_PGML
+Find the absolute maximum and absolute minimum values of  the function
+[```  f(x) = [$f] ```]
+on each of the indicated intervals.
 
-ANS(@answers);
+Enter 'DNE' for any absolute extremum that does not exist.
+
+a) The interval [`[[$p1],0]`]
+    * Absolute maximum = [_]{$ans1}{5}
+    * Absolute minimum = [_]{$ans2}{5}
+b) The interval [`[[$p2],[$p4]]`]
+    * Absolute maximum = [_]{$ans3}{5}
+    * Absolute minimum = [_]{$ans4}{5}
+c) The interval [`[[$p1],[$p4]]`]
+    * Absolute maximum = [_]{$ans5}{5}
+    * Absolute minimum = [_]{$ans6}{5}
+END_PGML
 
 ENDDOCUMENT();        # This should be the last executable line in the problem.