1. The problem statement, all variables and given/known data Let f be a function with derivatives of all orders and for which f(2)=7. When n is odd, the nth derivative of f at x=2 is 0. When n is even and n=>2, the nth derivative of f at x=2 is given by f(n) (2)= (n-1)!/3n a. Write the sixth-degree Taylor polynomial for f about x=2. b. In the Taylor series for f about x=2, what is the coefficient of (x-2)(2n) for n =>1 ? c. Find the interval of convergence of the Taylor series for f about x=2. Show the work that leads to your answer 2. Relevant equations Taylor series 3. The attempt at a solution a. I got the sixth-degree series. b. Will it just be (n-1)!/3n / (2n)! ?? c. So will the Taylor series be [tex]\sum[/tex] (n-1)/3n * (x-2)^2n from n=1 to infinity ??