When bounding the error of an th–degree Taylor polynomial approximation of a function…

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

When bounding the error of an

n

th–degree Taylor polynomial approximation of a function centered at

x=0

, a student selects a constant

M

such that

|f^{(n+1)}(x)|\le M

for all

x

in a specified set in order to guarantee a maximum error on the interval

(-r,r)

. Which of the following best describes the set that should be used to determine

M

if the goal is to find the largest possible symmetric interval? (a)

(-r,r)

(b)

(-\infty,\infty)

(c)

[-r,r]

(d)

[0,r]