Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 12 - Section 12.3 - Higher Order Derivatives: Acceleration and Concavity - Exercises - Page 901: 5

Answer

$ -0.96x^{-1.6}$

Work Step by Step

$f''(x)=\displaystyle \frac{d}{dx}\left[\frac{df}{dx}\right]=\frac{d^{2}f}{dx^{2}}$ $\displaystyle \frac{dy}{dx}=\frac{d}{dx}[4x^{0.4}-x]= 4(0.4x^{0.4-1})-1=1.6x^{-0.6}-1$ $\displaystyle \frac{d^{2}y}{dx^{2}}=\frac{d}{dx}[ 1.6x^{-0.6}-1]=1.6(-0.6x^{-1.6})$=$ -0.96x^{-1.6}$
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