How to graph tangent plane and surface

[JosephK]

Homework Statement

Graph the surface and the tangent plane at the given point.
(Choose the domain and viewpoint so that you get a good view of
both the surface and the tangent plane.) Then zoom in until the
surface and the tangent plane become indistinguishable.

Homework Equations

The Attempt at a Solution

I tried using Scilab but I didn't know how to use it. Does this problem require a computer or can I graph by hand? I tried to plug in points for x and y trying to keep points close together. By close I mean 1, -1, and 0. How do I form a plane from these points?

 

[Mark44]

Homework Statement

Graph the surface and the tangent plane at the given point.
(Choose the domain and viewpoint so that you get a good view of
both the surface and the tangent plane.) Then zoom in until the
surface and the tangent plane become indistinguishable.

Homework Equations

The Attempt at a Solution

I tried using Scilab but I didn't know how to use it. Does this problem require a computer or can I graph by hand? I tried to plug in points for x and y trying to keep points close together. By close I mean 1, -1, and 0. How do I form a plane from these points?

What is the equation of the surface? You forgot to include the problem description.

You should be able to sketch a graph of the surface and tangent plane without needing to use computer software.

 

[HallsofIvy]

If you were to graph "by hand" you are going to have a hard time "zooming" in!
There is a free on-line 3 d graphing program at
http://fooplot.com/index3d.php?

I haven't tried it myself.

 

[JosephK]

What is the equation of the surface? You forgot to include the problem description.

You should be able to sketch a graph of the surface and tangent plane without needing to use computer software.

z = x^2 + xy + 3y^2 (1, 1, 5)

Tangent plane I found: z = 3x +7y -5

Thank you!