# Problem3

Prep Main Page > Web Conference 2 > Sample Problems > Problem 3

```# DESCRIPTION
# Sample problem for WeBWorK PREP workshop
# Model problem:
# Determine if the function f(x) = sin(x^3)/x is positive,
# negative, or zero, and increasing, decreasing, or neither
# at x=2.
# WeBWorK problem written by Gavin LaRose, <glarose@umich.edu>
# ENDDESCRIPTION

DOCUMENT();

"PGstandard.pl",
"parserPopUp.pl",
"MathObjects.pl",
);

############################################################
# problem set-up
Context("Numeric");

# randomize
\$r = random(2,5,1);
\$p = random(1,5,1);

# the function
\$f = Compute("sin(x^\$r)/x");

\$fd = \$f->D();
\$fp = \$f->eval(x=>\$p);
if ( \$fp > 0 ) {
\$ans1 = 'positive';
} elsif ( \$fp < 0 ) {
\$ans1 = 'negative';
} else {
\$ans1 = 'zero';
}
\$sign = PopUp( [ '?', 'positive', 'negative', 'zero' ], \$ans1 );

\$fdp = \$fd->eval(x=>\$p);
if ( \$fdp > 0 ) {
\$dsgn = 'is positive';
\$ans2 = 'increasing';
} elsif ( \$fdp < 0 ) {
\$dsgn = 'is negative';
\$ans2 = 'decreasing';
} else {
\$dsgn = 'is zero';
\$ans2 = 'neither increasing nor decreasing';
}

\$deriv = PopUp( [ '?', 'increasing', 'decreasing',
'neither increasing nor decreasing' ], \$ans2 );

############################################################
# text

TEXT(beginproblem());
Context()->texStrings;
BEGIN_TEXT

Determine the sign and behavior of the function \(f(x) = \$f\)
at the point \(x = \$p\).
\$BR
At \(x = \$p\), the function is \{ \$sign->menu() \} and

END_TEXT
Context()->normalStrings;

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

ANS( \$sign->cmp() );
ANS( \$deriv->cmp() );

Context()->texStrings;
SOLUTION(EV3(<<'END_SOLUTION'));
\$PAR SOLUTION \$PAR
At the point \(x = \$p\), the function \(f(x) = \$f\) has the
value \(f(\$p) = \$fp\), which is \{ \$sign->correct_ans() \}.
The derivative of \(f\) is \(f'(x) = \$fd\), so that
\(f'(\$p) = \$fdp\) \$dsign, and \(f\) is \{ \$deriv->correct_ans() \}.

END_SOLUTION
Context()->normalStrings;

ENDDOCUMENT();

# end of problem
############################################################
```