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: 37

Answer

The slope at the point $(0, 0)$ is $3$.

Work Step by Step

To find the derivative of $y$, we find the derivative of the smaller functions and we add them together. The derivative of $4sin(\theta)$ is $4cos(\theta)$ ( you should remember that $(sin(x)'=cos(x))$ and that $(cos(x)'=-sin(x))$). The derivative of $-\theta$ is $-1$. Adding everything together gives $y' = 4cos(\theta)-1$. To find the slope, substitute the x-coordinate into the derivative. Plugging in $\theta = 0$ gives us $y' = 4cos(0)-1 = 4-1 = 3$ hence the slope at the point $(0, 0)$ is $3$.
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