Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 2 - Limits - 2.1 The Idea of Limits - 2.1 Exercises - Page 59: 6


The graph is in the figure below. This is because $f(x)=x^2$ is an even function. The slope at $x=0$ is equal to $0$.

Work Step by Step

The graph is in the figure below along with some of the secants and the tangent at $x=0$ (which is actually the $x$ axis!). This is because $f(x)=x^2$ is an even function i.e. it has the property that $f(-x)=f(x)$ because $(-x)^2=x^2$. Because of this, $f(a)=f(-a)$ so the points $(a,f(a))$ and $(-a,f(-a))$ will be at the same height above the $x$ axis and its slobe will be zero (i.e. it is parallel to the $x$ axis). The slope at $x=0$ is also $0$ because if we make $a$ smaller and smaller those secants will become closer and closer to this tangent.
Small 1517956938
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.