# Thread: Proving an equation is non-differentiable?

1. ## Proving an equation is non-differentiable?

Hi,

How would I go about formally proving that a continuous equation e.g. y=|x| is non-differentiable at a point such as x=0?

I know what it looks like graphically with a sharp edge but how would the proof look like algebraically?

2. Show that $\lim _{h \to 0^ + } \frac{{\left| {0 + h} \right| - \left| 0 \right|}}{h} \ne \lim _{h \to 0^ - } \frac{{\left| {0 + h} \right| - \left| 0 \right|}}{h}$

3. Originally Posted by Plato
Show that $\lim _{h \to 0^ + } \frac{{\left| {0 + h} \right| - \left| 0 \right|}}{h} \ne \lim _{h \to 0^ - } \frac{{\left| {0 + h} \right| - \left| 0 \right|}}{h}$
Wouldn't they both converge to 0 on both sides of the curve?

4. Originally Posted by Kataangel
Wouldn't they both converge to 0 on both sides of the curve?
Neither of those limits is zero.