The proof in Exercise 70 guarantees that the Taylor polynomial and its derivatives agree with the function and its derivatives at x = c. Use the graphs and tables in Exercises to discuss what happens to the accuracy of the Taylor polynomial as you move away from x = c.

Data from in Exercise 70

Let P_n(x) be the nth Taylor polynomial for ƒ at c. Prove that P_n (c) = ƒ(c) and P^(k)(c) = ƒ^(k) (c) for 1 ≤ k ≤n.