Thread: Odd Question

Aight, here's the question:

"Using the definition of derivative, find the derivative of the following function:

y= lxl (hint; rewrite this function as a piece-wise function first)"

I have managed to write it as a piece-wise, but I'm not sure what I'm supposed to do from that point. Thanks in advance for any help!

Just differentiate it piece-wise as well.

You should have f(x) = |x| = x if x>=0 or f(x) = |x| = -x if x < 0.

For x < 0 what will the derivative be? For x > 0 what will the derivative be? For x = 0, take a look at the graph of |x|. Does it look like the derivative will exist there? Also for x = 0, look at the one-sided limits for
f(0 + h)/h