Calculus 10th Edition

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

Chapter 6 - Differential Equations - 6.1 Exercises - Page 404: 53

Answer

\begin{array}{|c|c|c|c|c|c|} \hline x & {-4} & {-2} & {0} & {2} & {4} & {8} \\ \hline y & {2} & {0} & {4} & {4} & {6} & {8} \\ \hline \frac{d y }{ d x} & {-4} & {\text { Undef. }} & {0} & {1} & {\frac{4}{3}} & {2} \\ \\ \hline \end{array}

Work Step by Step

Given$$\dfrac{dy}{dx}=\frac{2x}{y}$$ and \begin{array}{|c|c|c|c|c|c|}\hline x & {-4} & {-2} & {0} & {2} & {4} & {8} \\ \hline y & {2} & {0} & {4} & {4} & {6} & {8} \\ \hline d y / d x & { } & { } & { } & { } & { } & { } \\ \hline\end{array} $$$$ Since the $1^{st}$ derivative $(\dfrac{dy}{dx}) $ mean the slope, so by substituting by the values of points we get, \begin{array}{|c|c|c|c|c|c|} \hline x & {-4} & {-2} & {0} & {2} & {4} & {8} \\ \hline y & {2} & {0} & {4} & {4} & {6} & {8} \\ \hline \frac{d y }{ d x} & {-4} & {\text { Undef. }} & {0} & {1} & {\frac{4}{3}} & {2} \\ \\ \hline \end{array}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.