Answer
See below.
Work Step by Step
A positive average rate of change only implies here that $f(5)\gt f(2)$ but it says nothing about the exact behavior between $2$ and $5$, thus it is not necessarily increasing over the whole interval.
College Algebra (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0321979478
ISBN 13:
978-0-32197-947-6
Chapter 3 - Section 3.3 - Properties of Function - 3.3 Assess Your Understanding - Page 236: 101
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