**
**

**On the mapping diagram a one sided derivative can be visualized using focus
points for the average rates that converge to a single focus point from only one side of the key number of interest for
the best linear approximating function for that side. **

**A one sided derivative can also be visualized as a vector on the target of the mapping diagram. **

In the figure the vector shown is for $f'_+(1)$.

For $x \ne 1$, in the example in the figure, the one sided derivatives are equal, so $f'_+(x)=f'\_(x)=f'(x)$.