Chapter 6.6, Problem 14P

For Problems 10 to 14, use a computer as needed to make plots of the given surfaces and the isothermal or equipotential curves. Try both $3\text{D}$ graphs and contour plots.

(a) Suppose that a hill (as in Fig. 5.1 ) has the equation $z=32-x^2-4y^2$, where $z=$ height measured from some reference level (in hundreds of feet). Sketch a contour map (that is, draw on one graph a set of curves $z=$ const.) ; use the contours $z=32,19,12,7,0$.

(b) If you start at the point $(3,2)$ and in the direction $i+j,$ are you going uphill or downhill, and how fast?