Chapter 12.4, Problem 69E

(a)

To determine

To compute: The values of $z_x$ and $z_y$.

(b)

To determine

To sketch: The level curves for $z=1,2,3\text{and}4$.

(c)

To determine

To explain: The changes in z values when it moves along the horizontal line $y=1$ in the xy-plane observation and also explain how this values are consistent with $z_x$.

(d)

To determine

To explain: The changes in z values when it moves along the vertical line $x=1$ in the xy-plane observation and also explain how this values are consistent with $z_y$.