# What is a corner in calculus?

##### 1 Answer

A derivative at a specified point is only defined for a function where there is only one slope at that specified point. A **corner** is one type of shape to a graph that has a different slope on either side. It is similar to a **cusp**.

You may see corners in the context of absolute value functions, like:

graph{-|x| + 2 [-10, 10, -5, 5]}

Here, the derivative at

Similarly, a cusp looks like this:

graph{2sqrt(|x|) [-10, 10, -5, 5]}

As you can see, it also has two different (and undefined) slopes at

If you're curious, the derivative of