Answer
$f(x)=x^{3}$, $a=5$
Work Step by Step
$f'(a)=\lim\limits_{h \to 0}\frac{f(a+h)-f(a)}{h}=\lim\limits_{h \to 0}\frac{(5+h)^{3}-125}{h}\,\,\,\,$ (given)
$\implies f(a+h)=(5+h)^{3}$ and $f(a)=125=5^{3}$
which gives $f(x)=x^{3}$ and $a=5$.
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 3 - Differentiation - 3.1 Definition of the Derivative - Exercises - Page 104: 53
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