# Problem2

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

```# DESCRIPTION
# Sample problem for WeBWorK PREP workshop
# Model problem:
# Identify all points where the function f(x) = |x| + |x-1| is
# non-differentiable.
# WeBWorK problem written by Gavin LaRose, <glarose@umich.edu>
# ENDDESCRIPTION

DOCUMENT();

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

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

# pick the points where we have the corner for the absolute value
#    functions
\$x0 = random(-3,-1,1);
\$x1 = random(1,3,1);

# the function
\$f = Compute("abs(x-\$x0) + abs(x-\$x1)")->reduce();

# the points
\$points = List( Compute(\$x0), Compute(\$x1) );

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

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

Identify all points where the function \(f(x) = \$f\)
is non-differentiable.  \${BITALIC}(Enter your point or
points as a comma-separated list.  For example, if your
answer is \(x = 3\) and \(x = 4\), you would enter
\${BBOLD}3, 4\$EBOLD.)\$EITALIC
\$PAR
Points \(x = \) \{ \$points->ans_rule(25) \}

END_TEXT
Context()->normalStrings;

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

ANS( \$points->cmp() );

Context()->texStrings;
SOLUTION(EV3(<<'END_SOLUTION'));
\$PAR SOLUTION \$PAR
The points of non-differentiability are \(x = \$points\).

END_SOLUTION
Context()->normalStrings;

ENDDOCUMENT();

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