Answer
It is possible.
Work Step by Step
Take $f(x)=-x^{2}+3$ on the interval $(-2,-1)$.
$f(x)\gt0$
$f'(x)=-2x\gt0$ on $(-2,-1)$
$f''(x)=-2\lt0$
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 4 - Applications of the Derivative - 4.2 What Derivatives Tell Us - 4.2 Exercises - Page 256: 9
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