## 6.6. A Function Primer

### C(n) Function

*g*is

*n*-times differentiable, the

*n*-th derivative is continuous, and

*g*is not

*(n+1)*-times differentiable.

On the right are the graphs of this root function for |

### Proof:

This proof is left as an exercise. As a hint, start with*n = 1*. The example, if correct, says that for

*n = 1*the function

*g*is once differentiable, the derivative is continuous, but not differentiable again. Why ? Then try

*n = 2*. Then, maybe, try an induction argument to prove the general case.