Answer
The function $f$ must have derivatives of all orders at the point $a$
Work Step by Step
A function $f$ has a Taylor series centered in $a$ if the function $f$ has derivative $f^{k} (a)$ of all orders at the point $a$.
Calculus: Early Transcendentals (2nd Edition)
by Briggs, Bill L.; Cochran, Lyle; Gillett, Bernard
Published by
Pearson
ISBN 10:
0321947347
ISBN 13:
978-0-32194-734-5
Chapter 9 - Power Series - 9.4 Working with Taylor Series - 9.4 Exercises - Page 702: 6
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