Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.2 Exponential Functions and Their Derivatives - 6.2 Exercises - Page 419: 57


$-4, -2$

Work Step by Step

$y=e^{rx}$ $y'=e^{rx}\frac{d}{dx}(rx)$ $y'=re^{rx}$ $y''=re^{rx}\frac{d}{dx}(rx)$ $y''=r^2e^{rx}$ $y''+6y'+8y=0$ $r^2e^{rx}+re^{rx}+8e^{rx}=0$ $r^2+r+8=0$ $(r+4)(r+2)=0$ So $r=-4$ and $r=-2$ are the solutions.
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