# Math Help - Is y= x^2-|x-4| differentiable at x=4?

1. ## Is y= x^2-|x-4| differentiable at x=4?

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

2. Originally Posted by -DQ-
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:
$
y=x^2 - x +4
$

and its derivative is: 2x-1

for x<4:
$
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.