# Can a function be continuous and non-differentiable on a given domain??

##### 2 Answers

Yes.

#### Explanation:

One of the most striking examples of this is the Weierstrass function, discovered by Karl Weierstrass which he defined in his original paper as:

#sum_(n=0)^oo a^n cos(b^n pi x)#

where

This is a very spiky function that is continuous everywhere on the Real line, but differentiable nowhere.

Yes, if it has a "bent" point. One example is

#### Explanation:

Continuous function practically means drawing it without taking your pencil off the paper. Mathematically, it means that for any

where the minus sign means approaching from left and plus sign means approaching from right.

Differentiable function practically means a function that steadily changes its slope (NOT at a constant rate). Therefore, a function that is non-differentiable at a given point practically means that it abruptly changes it's slope from the left of that point to the right.

Let's see 2 functions.

**Graph**

graph{x^2 [-10, 10, -5.21, 5.21]}

**Graph (zoomed)**

graph{x^2 [0.282, 3.7, 3.073, 4.783]}

Since at

**Graph**

graph{absx [-10, 10, -5.21, 5.21]}

At