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

Hi, I have this function:

f(x ) = 0 (x is irrational) or f(x) = 1/q for rational p/q in lowest terms.

show that this function is not differentiable anywhere

3. The attempt at a solution

This is the answer from the solutions book:

consider [(f(a+h) - f(a ) ) / h ]. function f is discontinuous at rational numbers, so we only have to look at irrational a.

if h is rational, then f(a+h) - f(a ) = 0

if h is irrational, then let a = m.a1a2a3...an and h = -0.00...an+1

Then, a + h = m1.a1a2a3..an0000 and f(a+h) > 10^(-n)

My question is.. how do we know anything about f(a+h)? a+h is > 10^(-n) but what is f(a+h)?

thanks

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

Dismiss Notice

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: 0 when irrational, 1/q in lowest terms with rational not differentiable.

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