Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.5 - Zeros of Polynomial Functions - Exercise Set - Page 380: 94



Work Step by Step

From the graph, the function is increasing as the value of $x$ is increasing, other than at the point $x=0$. At $x=0$ the slope of the graph is zero, and that point is known as the point of inflection. So, the number of turning points is $2$. $\begin{align} & \text{Smallest}\ \text{degree}\ \text{of}\ \text{polynomial}=\left( \text{Number}\ \text{of}\ \text{turning}\ \text{point} \right)\text{+1} \\ & =2+1 \\ & =3 \end{align}$ Hence, the smallest degree of the polynomial is $3$.
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