## 6.6. A Function Primer

### C(1) Function

This is the graph of the function. Zoom in by clicking and
dragging the mouse, or select |

### Proof:

We have studied this function before. The details are left as an exercise, but here is the idea:

*g*is differentiable for all non-zero*x*(apply some theorems)- find the derivative for non-zero
*x*by using chain and product rules - find the derivative of
*g*at zero by looking at the limit of the difference quotient at zero - show that the derivative you have just found is not continuous
at zero by considering left and right limits as
*x*approaches zero