What is an example of a continuous non-differentiable function?

Answer 1

y = x^(2/3) is continuous but non-differentiable at x = 0.

y = |x| is also.

Answer 2

A very classic example is f(x) = |x|. It's continuous everywhere on R, but not differentiable at x = 0. A simple calculation shows that the derivative to the left is -1 and to the right is 1 So, f is not diffrenetiable at x = 0.

There's a more complicated example, givem by a series of functions, that is continuous everywhere but nowhere differentiable.

Answer 3

Geometric Brownian Motion is continuous and nowhere differentiable.

It is used to model stock prices, and is "jagged." The closer you zoom in on any area, the more jaggedness becomes apparent.

Stochastic calculus sort of gets around this, but it's unlikely you'd like to hear about it . . . ..

Answer 4

The Weierstrass function: http://en.wikipedia.org/wiki/Nowhere_differentiable

It's continuous, but on any given interval their are an infinite of local minima and maxima.

Answer 5

T72e3dc8bc34edef2b3364cc1bec0afe72e3dc8bc34edef2b3364cc1bec0afderivative72e3dc8bc34edef2b3364cc1bec0afisn't72e3dc8bc34edef2b3364cc1bec0afde72e3dc8bc34edef2b3364cc1bec0afined72e3dc8bc34edef2b3364cc1bec0afat72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af=72e3dc8bc34edef2b3364cc1bec0af072e3dc8bc34edef2b3364cc1bec0afbecause72e3dc8bc34edef2b3364cc1bec0afyou72e3dc8bc34edef2b3364cc1bec0afcan't72e3dc8bc34edef2b3364cc1bec0aftake72e3dc8bc34edef2b3364cc1bec0aft72e3dc8bc34edef2b3364cc1bec0afe72e3dc8bc34edef2b3364cc1bec0aflimit72e3dc8bc34edef2b3364cc1bec0afo72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af[72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af-72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af]/72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0afin72e3dc8bc34edef2b3364cc1bec0afbot72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0afdirections72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0afrom72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af=72e3dc8bc34edef2b3364cc1bec0af0.72e3dc8bc34edef2b3364cc1bec0afT72e3dc8bc34edef2b3364cc1bec0afat72e3dc8bc34edef2b3364cc1bec0aflimit72e3dc8bc34edef2b3364cc1bec0afonly72e3dc8bc34edef2b3364cc1bec0afe72e3dc8bc34edef2b3364cc1bec0afists72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0afor72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af->72e3dc8bc34edef2b3364cc1bec0af072e3dc8bc34edef2b3364cc1bec0af,72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0af72e3dc8bc34edef2b3364cc1bec0afdecreasing72e3dc8bc34edef2b3364cc1bec0afto72e3dc8bc34edef2b3364cc1bec0af0.