When bounding the error of an nth–degree Taylor polynomial approximation of a function centered at x=0, a student selects a constant M such that ∣f(n+1)(x)∣≤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) (−∞,∞)
c) [−r,r]
d) [0,r]