Determine the Maximum Error Guaranteed by Taylor's Theorem with Remainder $e ^ { - x }$

Multiple Choice

Determine the maximum error guaranteed by Taylor's Theorem with Remainder when the fifth-degree Taylor polynomial is used to approximate $e ^ { - x }$ in the interval $[ 0,1 ]$ centered at 0. Round your answer to five decimal places.

A) 0.02139
B) 0.00339
C) 0.00833
D) 0.00139
E) 0.05139