Tangent Planes and How to Build Them

Tangent lines were important in single variable calculus because they give a good way to approximate a complicated function with a simple function near a given point. Similarly, tangent planes give a good way to approximate complicated 2-variable functions with a simple function, but how do you set up the equation for a tangent plane?

~~~
This video was funded by Texas A&M University as part of the Enhancing Online Courses grant.

~~~
The animations in this video were mostly made with a homemade Python library called "Morpho". You can find the project here:

[witoldradzik]

"Explain it to me like i'm five" done correctly, thanks a lot! <3

[clockel]

This was a concise and insightful explanation, bravo!

[dezmania]

Cramming for finals you're a big help man thanks so much

[bubb]

This probably saved me a lot of time, thanks! You made it very easy to understand

[abrahammekonnen]

This video is a really nice review. Thank you

[spdas]

After long search ultimately I got the answer of the junction point of single variable to double variable that leads to multivariable view point of grad and tangent point. Many thanks. Kindly upload a video of direction of the gradient and actual line of ascent on the surface with an example (with 3D graph) of an paraboloid. ❤from 🇮🇳🙏.

[mohamedmouh]

thank you so much. it's so helpful 🥰

[kishores]

No, two independent lines do not uniquely define a plane. In three-dimensional space, a plane is defined by at least three non-collinear points. The reason is that a single line can be drawn through any two points, and multiple lines can be parallel to each other while lying in different planes.

To uniquely determine a plane, you need three points that are not collinear (meaning they are not on a single straight line). These three points can then be used to form a unique plane in three-dimensional space.

[finfin]

9th grade has been killing me so far thank you so much!!!