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: 34


The slope at the point $(1, -1)$ is $8$.

Work Step by Step

The function is the sum of "smaller" functions hence the overall derivative is the sum of the derivative of the smaller functions. The derivative of $2x^4$, using the power rule$((x^n)'=nx^{n-1})$, is $(2)(4)(x^{4-1})$ which when simplified is equal to $8x^3$. The derivative of $-3$ is 0. The overall derivative is therefore equal to $8x^3$. To evaluate the derivative substitute in the x-coordinate. Plugging in $1$ gives $(8)(1)$ which is equal to $8$.
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