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 902: 24

Answer

No inflection points (concave down everywhere).

Work Step by Step

A curve is concave up if its slope is increasing, in which case the second derivative is positive. A curve is concave down if its slope is decreasing, in which case the second derivative is negative. A point in the domain of $f$ where the graph of $f$ changes concavity, from concave up to concave down or vice versa, is called a point of inflection. At a point of inflection, the second derivative is either zero or undefined. ---- Observing from left to right, From being very steep and positive, the slope becomes gentler (decreases), while remaining positive on the whole domain. No change in concavity. No inflection points (concave down everywhere)
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