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

Answer

False

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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.