Question

Use a Computer to Graph the Function using various domains and viewpoints.

\(f\left( {x,y} \right) = x{y^3} - y{x^3}\) (Dog Saddle)

Short answer

Hence, from the 2 figures, graph is veryflat near the originand the contour linesdeviatefrom the origin.

Step-by-step solution

Maple input:

\(\begin{aligned}{l} > with(plots)\\ > plot3d(x{y^3} - y{x^3},x = - 2.2,y = - 2.2)\end{aligned}\)

Maple Output:

\(\begin{aligned}{l} > with(plots)\\ > plot3d(x{y^3} - {x^3},x = - 2.2,y = - 2.2)\end{aligned}\)

Sketching The Contour Lines

Maple Input:

\(\begin{aligned}{l} > with(plots)\\ > contourplot(x{y^3} - y{x^3},x = - 3.3,y = - 3.3)\end{aligned}\)

Hence, from the 2 figures, graph is veryflat nearthe originand the contour linesdeviatefrom the origin.