# 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");
$showPartialCorrectAnswers = 1; # randomize$r = random(2,5,1);
$p = random(1,5,1); # the function$f = Compute("sin(x^$r)/x"); # the answers$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
\{ $deriv->menu() \}. END_TEXT Context()->normalStrings; ############################################################ # answer and solution ANS($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
############################################################