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

Quote:

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:
$<br /> y=x^2 - x +4<br />$
and its derivative is: 2x-1

for x<4:
$<br /> y=x^2+x-4<br />$
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.

cool. it's weird because the graph looks like it doesn't but it does when you prove it like that.