(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Define h(x)=x^3sin(1/x) for x[tex]\neq[/tex]0. and h(0)=0. Show h is differentiable everywhere and that h is cont everywhere, but fails to have a derivative at one point.

2. Relevant equations

3. The attempt at a solution

[h(x)-h(0)]/[x-0]=x^2sin(1/x)

h is diff everywhere because the limit exists and we know x[tex]\equiv[/tex]0.

h'(x)=3x^2sin(1/x)-xcos(1/x)

We know f is diff at [tex]x_{0}[/tex], then f must be continuous at [tex]x_{0}[/tex].

h has a derivative at x if x[tex]\neq[/tex]0.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Show h is differentiable

**Physics Forums | Science Articles, Homework Help, Discussion**