When using a Taylor polynomial centered at to approximate a differentiable function

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

Problem

When using a Taylor polynomial centered at

x=a

to approximate a differentiable function

f

, which of the following changes is most likely to decrease the approximation error at a fixed point

x

? (a) Increasing the distance between

x

and

a

while keeping the degree fixed (b) Decreasing the degree of the polynomial while keeping

x

fixed (c) Increasing the degree of the polynomial while keeping

x

fixed (d) Increasing both the distance between

x

and

a

and the degree of the polynomial by the same amount