# Thread: Derivative of piecewise functions...halp!

1. ## Derivative of piecewise functions...halp!

So the problem goes like this:

Let f(x) be -x^3 at x<0 and x^3 at x>=0.

I need to find the first derivative, second derivative, and the third derivative both the points which they are undefined and their graphs.

2. Originally Posted by deth2munkies
So the problem goes like this:

Let f(x) be -x^3 at x<0 and x^3 at x>=0.

I need to find the first derivative, second derivative, and the third derivative both the points which they are undefined and their graphs.

I'm a little confused by what you mean by "both the points which they are undefined". As you have written it this function is defined everywhere, and so are the derivatives.

To take derivatives of piecewise functions you take the derivative of each piece and keep the bounds on x the same.

For instance,
if f(x) = 2x for x<0 and f(x)=x^2 for x>=0 then
the first derivative will be
f'(x)=2 for x<0 and f'(x)=2x for x>=0.

Hope this helps with your problem!

3. Originally Posted by ziggychick
I'm a little confused by what you mean by "both the points which they are undefined". As you have written it this function is defined everywhere, and so are the derivatives.

To take derivatives of piecewise functions you take the derivative of each piece and keep the bounds on x the same.

For instance,
if f(x) = 2x for x<0 and f(x)=x^2 for x>=0 then
the first derivative will be
f'(x)=2 for x<0 and f'(x)=2x for x>=0.

Hope this helps with your problem!
Alright, thanks.

I was only supposed to find the points where the third derivative was undefined, although I realize I didn't word it the best way.