I asked about the first part of this problem in https://www.physicsforums.com/showthread.php?t=592408. I thought the best idea was to start another thread for the second part. 1. The problem statement, all variables and given/known data Part a) Given f(x)=ax+b, and f(3)(x)=64x+21, find the values of the constants a and b. (note: f(3)(x) means fff(x)) I figured out a=4 and b=1 Part b) Suggest a rule for f(n)(x). 2. Relevant equations f(3)(x)=a3x+b(a2+a+1) 3. The attempt at a solution From the equation I got in the first part (above) I reasoned that the genereal rule would be: f(n)(x)=anx+b(an-1+an-2...a+1) a=4 and b=1 so, f(n)(x)=4nx+(4n-1+4^n-2...4+1) However that isn't a very good general rule and the answer given in the book is: 4nx+(4n-1)/3 I have no idea how to reach that from what I've got now.