Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Section 3.2 - The Derivative as a Function - Exercises 3.2 - Page 117: 41



Work Step by Step

Step 1. To determine if the piecewise defined function is differentiable at the origin, we need to make sure that the function is continuous at the origin and the left and right derivatives are equal. Step 2. Right side: $\lim_{x\to0^+}f(x)=2(0)-1=-1$ Step 3. Left side: $\lim_{x\to0^-}f(x)=0^2+2(0)+7=7$ Step 4. Since the left and right limits are not equal, the function is not differentiable at the origin.
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.