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

Answer

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 $0$.
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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.
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