Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.2 Exercises: 32

Answer

The slope at the point $(4, 1)$ is $\frac{1}{4}$.

Work Step by Step

First rewrite the function as $2-4t^{-1}$. This function is the sum of "smaller" functions hence the overall derivative is the sum of the derivative of the smaller functions. The derivative of 2 is 0. The derivative of $-4t^{-1}$ is equal to $(-4)(-1)(t^{-1-1})$ which is equivalent to $\frac{4}{t^{2}}$. To evaluate the derivative substitute in the x-coordinate. Plugging in $4$ gives us $\frac{4}{16}$ which when simplified is $\frac{1}{4}$.
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