Simple dirichlet function differentiability

[Nanatsu]

Homework Statement

f(x) = {x, x rational, 0, x irrational

g(x) = {x^2, x rational, 0, x irrational

Show that f(x) is not differentiable at 0.
Show that g(x) is differentiable at 0

Homework Equations

f'(x) = lim(h->0) f(x+h) - f(x)/h I suppose

The Attempt at a Solution

Just wondering if I'm thinking right. For f(x) the difference quotient becomes h/0 as h-> 0 and with g(x) it becomes lim(h->0) h^2/h = lim(h->0) h = 0?

 

[LCKurtz]

"

Just wondering if I'm thinking right. For f(x) the difference quotient becomes h/0 as h-> 0

I suppose you mean h/h?

and with g(x) it becomes lim(h->0) h²/h = lim(h->0) h = 0?"

That's the general idea, but you have to consider the fact that h may be rational or irrational in a careful writeup.