Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Preliminary Questions - Page 326: 5


$(0,1) \cup (1,\infty)$

Work Step by Step

The function $y=b^x$ is concave up when $y''$ is positive. We see that: $y''=b^x(\ln b)^2\ge0$ Note that for $b=1$, the graph is not concave up $(y''=0)$ because the graph is a straight line ($y=1^x=1$). Thus, $y$ is concave up for any value of $b$ except $1$: $(0,1) \cup (1,\infty)$
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