Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.2 Exercises: 87



Work Step by Step

Counter-example: let $ f(x)=6x+4; g(x)=6x+7$. Using the power rule, $f'(x)=6 ; g'(x) =6$. While the derivatives are the same, the functions are clearly not the same. Explanation: When differentiating, the constant gets lost so two functions that have the same derivative will have the same terms down to and including $x$, but the constant could be different. In fact, two functions that have the same derivative belong to a family of functions but are not necessarily the same function.
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