Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.8 - The Derivative as a Function - 2.8 Exercises - Page 163: 45

Answer

When we zoom in toward the point $(-1,0)$, we can see that the graph makes a smooth line through the point. This shows us that $f$ is differentiable at the point $(-1,0)$ When we zoom in toward the origin at $(0,0)$, we can see that the graph comes to a sharp point. This shows us that $f$ is not differentiable at the point $(0,0)$

Work Step by Step

$f(x) = x+\sqrt{\vert x \vert}$ When we zoom in toward the point $(-1,0)$, we can see that the graph makes a smooth line through the point. This shows us that $f$ is differentiable at the point $(-1,0)$ When we zoom in toward the origin at $(0,0)$, we can see that the graph comes to a sharp point. This shows us that $f$ is not differentiable at the point $(0,0)$
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