# What are some examples of non differentiable functions?

##### 1 Answer

There are three ways a function can be non-differentiable. We'll look at all 3 cases.

**Case 1**

A function in non-differentiable where it is discontinuous.

Example (1a) f

graph{y=cotx [-10, 10, -5, 5]}

Example (1b)

Note that

Unfortunately, the graphing utility does not show the holes at

graph{(x^3-6x^2+9x)/(x^3-2x^2-3x) [-10, 10, -5, 5]}

Example 1c) Define

Example 1d) description : Piecewise-defined functions my have discontiuities.

**Case 2**

A function is non-differentiable where it has a "cusp" or a "corner point".

This occurs at

Example 2a)

(This function can also be written:

graph{abs(x-2) [-3.86, 10.184, -3.45, 3.57]}

Example 2b)

graph{x+root(3)(x^2-2x+1) [-3.86, 10.184, -3.45, 3.57]}

**Case 3**

A function is non-differentiable at

Example 3a)

graph{2+(x-1)^(1/3) [-2.44, 4.487, -0.353, 3.11]}

Example 3b) For some functions, we only consider one-sided limts:

graph{sqrt(4-x^2) [-3.58, 4.213, -1.303, 2.592]}

Example 3c)

graph{x^(2/3) [-8.18, 7.616, -2.776, 5.126]}

Here's a link you may find helpful:

http://socratic.org/calculus/derivatives/differentiable-vs-non-differentiable-functions