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: 31


The slope at the point $(2, 2)$ is$-2$

Work Step by Step

The graphical definition of the derivative is the slope at a point; hence, whenever you read slope at a point, you need to find the derivative. To find the derivative of $\frac{8}{x^2}$; rewrite it as $8x^{-2}$ then using the power rule, the derivative is $(8)(-2)(x^{-2-1})$ which when simplified is $-\frac{16}{x^3}$. To find the slope at the required point, substitute the x-coordinate into the derivative. Plugging in 2 in the derivative gives us $-\frac{16}{8}$ which is $-2$.
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