Calculus Concepts: An Informal Approach to the Mathematics of Change 5th Edition

Published by Brooks Cole
ISBN 10: 1-43904-957-2
ISBN 13: 978-1-43904-957-0

Chapter 1 - Ingredients of Change: Functions and Limits - 1.8 Activities - Page 81: 2

Answer

1) for $f(x)$ $f\left( x\right) =1.2+3\ln x=a+b\ln x\Rightarrow b=+3$ so $f(x)$ is increasing and concave down 2) for $g(x)$ $g\left( x\right) =-1.4+3\ln x=a+b\ln x\Rightarrow b=+3$ so $g(x)$ is increasing and concave down

Work Step by Step

İn a function like $f\left( x\right) =a+b\ln x$ if $b$ is positive then function is increasing and will be concave down 1) for $f(x)$ $f\left( x\right) =1.2+3\ln x=a+b\ln x\Rightarrow b=+3$ so $f(x)$ is increasing and concave down 2) for $g(x)$ $g\left( x\right) =-1.4+3\ln x=a+b\ln x\Rightarrow b=+3$ so $g(x) $ is increasing and concave down And when $x=1$ then $g(x)$ will be negative so we can easily match the graph
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