Recent content by jimmyly

I completely understand now! thank you so much for your help and clarity, I appreciate it!

sorry f' = (-(x+h) + (x+h) - (-x+x))/h = (-x - h + x + h + x - x)/h = 0/h not 2x/h

Yeah sorry for the confusion

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?

shouldn't f'(0) = 0 or undefined or dne since there is no derivative at 0?

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

So how do I show that mathematically? I understand that geometrically, but when I do problems like these I have a tough time doing it

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...

Thank you! :)

Wow that's amazing. Thanks everyone! You are all wonderful

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!

oh that just did it didn't it?!

so from this I got |a + b| <= |a| + |b| |(x+y) + (-y)| <= |x+y| + |-y| |x + y - y| <= |x+y| + |-y| |x| - |y| <= |x + y|

understandable no worries we all make mistakes!

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? :)