Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 15 - Differentiation in Several Variables - 15.5 The Gradient and Directional Derivatives - Exercises - Page 802: 49

Answer

Please see the figure attached.

Work Step by Step

We use a computer algebra system to produce a contour plot of $f\left( {x,y} \right) = {x^2} - 3xy + y - {y^2}$ together with its gradient vector field on the domain $\left[ { - 4 \times 4} \right] \times \left[ { - 4 \times 4} \right]$. The result is shown in the figure attached.
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