Write f as piecewise defined function

[ludi_srbin]

Let f(x)=x+|x| and g be defined by the rule "g(x) is the slope of the graph pf f at x".

Write f as piecewise defined function.

 

[ludi_srbin]

Can I write it just like

f(x)={ x+|x| if x>1

 

[TD]

Where x > 0, you get f(x) = 2x.
Where x < 0, you get f(x) = 0.

Does that help?

 

[ludi_srbin]

O, got you. Thanks.

 

[honestrosewater]

Where x > 0, you get f(x) = 2x.
Where x < 0, you get f(x) = 0.

Does that help?

Minor point: don't forget x = 0 in your definition.

 

[ludi_srbin]

So should I put that also?

 

[TD]

Make the first one $$\ge$$ then ;o)

 

[ludi_srbin]

And If I want to find g I use derivative?

 

[TD]

Sure, you could do that. Should be quite simple in this case!

 

[ludi_srbin]

Yeah. Thanks for help.

 

[FluxCapacitator]

Just remember that your derivative doesn't exist at x=0. I've gotten points taken off because I wrote the derivative with less than or equal signs, even though it's supposed to have just a less than sign.