Exercise 5.  Let      be a polynomial of degree  .  

5 (a).  Show that  .  

Solution 5 (a).

See text and/or instructor's solution manual.

Solution.  Proof by mathematical induction.  

The result is clearly true when n=1.  

Assume for some    that  .  

Consider   .  

Since the derivative of the sum of two terms is the sum of the derivatives, we have  

                      

The induction assumption now gives the required result.

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell