Thanks for the replies! I fixed up the errors in my thread and added parentheses.
so I re-did the left for x<0
I got
f' = (-(x+h) + (x+h) - (-x+x))/h = (-x - h + x + h + x - x)/h = 2x/h but taking the limit as h->0 it is undefined
is it an algebraic error I am making?
also when I graph it out it only shows the right side / instead of V
I don't understand how I got the left derivative as -1 when there's nothing on the left
Homework Statement
f(x) = |x| + x
Does f'(0) exist? Does f'(x) exist for values of x other than 0?
This is from lang's a first course in calculus page 54 # 13
Homework Equations
lim (f(x+h) - f(x))/h
h->0
The Attempt at a Solution
So I'm not sure if I am doing this...
Would this be classified as a direct proof? I'm trying to learn proofs on my own so this is a little bit confusing to me. Thanks everyone for helping me out!
okay so here is what I'm doing right now
|x+y| >= |x| - |y|
with x = x + y - y
I got
|x + y| >= |x| + |y| - |y| - |y|
cancelling the |y|
|x + y| >= |x| + |y|
am I on the right track? :)