Is the Function x->|x| Differentiable at 0?

  • Context: Graduate 
  • Thread starter Thread starter losin
  • Start date Start date
  • Tags Tags
    Differentiability
Join the discussion
Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.
Real named experts · corrections over time · the nuance an AI answer skips
Sign up Log in
3 replies · 2K views
losin
Messages
12
Reaction score
0
I want to show x->abs(x) is not differentiable at 0

Some techniques in analysis are required... how should i do?
 
Physics news on Phys.org
Calculate left and right limit of the difference quotient. If the function were differentiable, these would coincide, but they don't.
 
More basically ... use the definition of derivative.
 

Similar threads

Is the Function $f(x,y)=\frac{x}{y}+\frac{y}{x}$ Differentiable and $C^1$?
  • evinda
  • · Replies 7 ·
  • Calculus
Replies
7
Undergrad Is ln(x) differentiable at negative x-axis
  • Miraj Kayastha
  • · Replies 4 ·
  • Calculus
Replies
4
Undergrad Is mod x differentiable at all points
  • sphyics
  • · Replies 6 ·
  • Calculus
Replies
6
Graduate Vector calculus - Prove a function is not differentiable at (0,0)
  • physics1000
  • · Replies 1 ·
  • Calculus
Replies
1
Undergrad F(x) differentiable at / near x=0?
  • Redbelly98
  • · Replies 5 ·
  • Calculus
Replies
5
Is the function F(x) = x^2*cos(pi/x) differentiable at x=0?
  • Rishavutkarsh
  • · Replies 4 ·
  • Calculus and Beyond Homework Help
Replies
4
Is f(x) Differentiable at x=0?
  • evinda
  • · Replies 4 ·
  • Topology and Analysis
Replies
4
Undergrad Is the function differentiable at x = p?
  • PcumP_Ravenclaw
  • · Replies 5 ·
  • Calculus
Replies
5
Show function series involving arctan is not differentiable at x=0
  • schniefen
  • · Replies 26 ·
  • Calculus and Beyond Homework Help
Replies
26
Is f(x,y) Differentiable at (0,0)?
  • Barioth
  • · Replies 2 ·
  • Calculus
Replies
2