University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 2 - Section 2.1 - Rates of Change and Tangents to Curves - Exercises - Page 56: 6


$\frac{\Delta y}{\Delta t}=0$

Work Step by Step

*Average rates of change: The average rate of change of $y=f(x)$ with respect to $x$ over the interval $[x_1,x_2]$ is: $$\frac{\Delta y}{\Delta x}=\frac{f(x_2)-f(x_1)}{x_2-x_1}$$ $$P(\theta)=\theta^3-4\theta^2+5\theta\hspace{1cm}[1,2]$$ The average rate of change of $y=P(\theta)$: $$\frac{\Delta y}{\Delta\theta}=\frac{(2^3-4\times2^2+5\times2)-(1^3-4\times1^2+5\times1)}{2-1}$$ $$\frac{\Delta y}{\Delta t}=\frac{(8-16+10)-(1-4+5)}{1}=2-2=0$$
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