Likely obvious but I just cant figure out why LaTeX is choking on this problem when I include the solution.

The table seems okay to me, but there must be an issue with the array.

++++++++++++++++++

## DESCRIPTION

## This is Problem 3.3.15 from the APEX Calculus text (3.3.16 in the ULETH APEX text). It covers the First Derivative Test.

## ENDDESCRIPTION

## DBsubject(Calculus - single variable)

## DBchapter(Applications of differentiation)

## DBsection(Increasing/decreasing functions and local extrema)

## Level(2)

## Institution('Valdosta State University')

## Author('S. V. Ault')

## RevisedBy('F. J. Francis')

## TitleText1('APEX Calculus')

## AuthorText1('Hartman')

## EditionText1('3.0')

## Section1('3.3')

## Problem1('15')

## MO(1)

## Keywords('first derivative test', 'increasing and decreasing functions','ULETH-MATH1560', 'ULETH-MATH1565')

###########################

# Initialization

DOCUMENT();

# Load whatever macros you need for the problem

loadMacros(

"PGstandard.pl",

"MathObjects.pl",

# Used to provide contextual help for how to type answers.

"AnswerFormatHelp.pl",

# Provides greater control over the layout of the problem.

"PGML.pl",

# Used for course-specific initializations.

"PGcourse.pl",

);

# Sets up basic problem information.

TEXT(beginproblem());

#############################

# Setup

#-ULETH-#

Context("Numeric");

$b = 3*random(1,6,1);

$c = random(1,20,1)*random(-1,1,2);

$f = Formula("x^3 + $b x^2 + $c")->reduce();

$b2 = 2*$b;

$df = Formula("3x^2 + $b2 x")->reduce();

Context("Interval");

@domain = Compute("(-INF, INF)");

$crit1 = -$b2/3;

$crit2 = 0;

@inc = Compute("(-INF, $crit1) U ($crit2, INF)");

@dec = Compute("($crit1, $crit2)");

$ans_crit = List($crit1, $crit2);

$ans_max = List($crit1);

$ans_min = List($crit2);

#-ENDULETH-#

#############################

# Problem Text

#-ULETH-#

BEGIN_PGML

In the following questions, consider the function

>>[`f(x) = [$f].`]<<

Enter *DNE* if an answer does not exist.

----

a) Give the domain of [`f`] (in interval notation): [________________________]{Compute(@domain)} [@ AnswerFormatHelp("intervals") @]*

b) Find the critical numbers of [`f`]. [____________]{Compute($ans_crit)} [@ AnswerFormatHelp("numbers") @]*

(Separate multiple answers with commas.)

c) Determine the intervals on which [`f`] is increasing and decreasing.

[`f`] is increasing on: [________________________]{Compute(@inc)}

[`f`] is decreasing on: [________________________]{Compute(@dec)}

d) Use the First Derivative Test to determine whether each

critical point is a relative maximum, minimum, or neither.

Relative maxima occur at [`x = `] [____________]{Compute($ans_max)} (Separate multiple

answers with commas.)

Relative minima occur at [`x = `] [____________]{Compute($ans_min)} (Separate multiple answers with commas.)

END_PGML

#-ENDULETH-#

#############################

# Solution

#-ULETH-#

BEGIN_PGML_SOLUTION

Since [`f(x) = [$f]`] is a polynomial, its domain is all real numbers,

or [`(-\infty, \infty)`].

Its derivative is [`f'(x) = [$df]`]. Factor to find the two critical numbers,

[`x = [$crit1], [$crit2]`].

Use the first derivative test, choosing sample points in each interval.

[``

\begin{array}{|l|l|l|}

\hline

\textrm{Interval} &

\textrm{Sign of}\; f'\; \textrm{at sample} &

\textrm{Conclusion} \\

\hline

\hline

(-\infty, [$crit1]) & \textrm{positive} & \textrm{increasing} \\

\hline

([$crit1], [$crit2]) & \textrm{negative} & \textrm{decreasing} \\

\hline

([$crit2], \infty) & \textrm{positive} & \textrm{increasing} \\

\hline

\end{array}

``]

Based on the signs in each interval there is a

relative maximum at [`x = [$crit1]`] and a

relative minimum at [`x = [$crit2]`].

END_PGML_SOLUTION

#-ENDULETH-#

#############################

# Answer evaluation

#Answers are evaluated in the problem text.

#-ULETH-#

# Setting this to 1 means that students will receive feedback on whether their

# answers are correct.

$showPartialCorrectAnswers = 1;

#-ENDULETH-#

COMMENT('

Randomization provides 240 possible versions of this question.<BR>

Includes a solution set.<BR>

Made from a ULETH template.<BR>

');

ENDDOCUMENT();