Chapter 14 - Partial Derivatives - 14.3 Partial Derivatives - 14.3 Exercises - Page 964: 7

(a) Positive (b) Negative

(a) The second derivative shows concavity. As we move along the x-axis at the point $(-1, 2)$ the graph is shown to be concave up . This shows that $f_{xx} $ is positive. (b) The second derivative shows concavity. As we move along the y-axis at the point $(-1, 2)$ the graph is shown to be concave down. This shows that $f_{yy} $ is negative.