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();

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

############################################################
# problem set-up
Context("Numeric");
$showPartialCorrectAnswers = 1;

# 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;

############################################################
# answer and solution

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