Let T n be the nth Taylor polynomial at x = a for a polynomial of

Let T_n be the nth Taylor polynomial at x = a for a polynomial ƒ of degree n. Based on the result of Exercise 59, guess the value of |ƒ(x) − T_n(x)|. Prove that your guess is correct using the Error Bound.

Data From Exercise 59

Let ƒ(x) = 3x³ + 2x² − x − 4. Calculate T_j for j = 1, 2, 3, 4, 5 at both a = 0 and a = 1. Show that T₃(x) = ƒ(x) in both cases.