Doesn't x^2 mean it'll be a parabola and thus differentiable for all x? That's what I thought but the absolutes screw me up
I guess you could follow this procedure:
for x > 4:
$\displaystyle
y=x^2 - x +4
$
and its derivative is: 2x-1
for x<4:
$\displaystyle
y=x^2+x-4
$
and its derivative is: 2x+1
lim(2x-1) for x approaches to 4+ is 7;
lim(2x+1) for x approaches to 4- is 9;
so y's derivative is not continuous at x=4, thus y is not differentiable at x=4.
may this help you.