College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 3 - Section 3.3 - Properties of Function - 3.3 Assess Your Understanding - Page 234: 78

Answer

$ a.\quad G$ is even. $ b.\quad$local maximum of $400$ at $x=-4$. $ c.\quad A=1612.8$ sq.units

Work Step by Step

$a.$ $G(-x)=-(-x)^{4}+32(-x)^{2}+144=-x^{4}+32x+144=G(x)$ $G(-x)=G(x)$, so the function is even. $b.$ Being even, its graph has y-axis symmetry. If $(4,400)$ is a local maximum point, then the point symmetric to it, $(-4,400)$ is on the graph and is also a local maximum point. $c.$ Because of symmetry relative to the y-axis, the area enclosed between $x=-6$ and the origin equals the area enclosed from the origin to $x=6$ $A=1612.8$ sq.units
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.