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

Printable View

- Jan 25th 2010, 06:56 AM-DQ-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

- Jan 25th 2010, 07:23 AMkylehk
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. - Jan 25th 2010, 09:31 AM-DQ-
cool. it's weird because the graph looks like it doesn't but it does when you prove it like that.