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?
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This video was funded by Texas A&M University as part of the Enhancing Online Courses grant.
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The animations in this video were mostly made with a homemade Python library called "Morpho". You can find the project here:
github.com/mor...

[@witoldradzik5589]

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

[@clock1el740]

This was a concise and insightful explanation, bravo!

[@dezgaming1988]

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

[@spdas5942]

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 🇮🇳🙏.

[@bubb5263]

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

[@mohamedmouh3949]

thank you so much. it's so helpful 🥰

[@sum1sw]

well done, thank you

[@dineshkumarv9493]

nice and easy explanation

[@user-mc1dp5oy8e]

Thank you❤

[@finfin4343]

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

[@quacki614]

how the hell are u taking multivariable calculus in 9th grade

[@KDYinYouTube]

​@@quacki614 I take that when I am 1st grade

[@kishores99]

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.

[@12degreesnowman11]

What we do in multi variable calculus is take 3 points, form 2 vectors with them and then take the cross product to find a normal to both of them. Then we use one point, the one they both share in common, and plug them in to the equation of a plane. The vector will be a,b,c… and the point will be x0,y0,z0….
Apparently a plane is defined by a vector normal to the plane and a point on the plane.

[@steefbroeder4421]

Hreo!

[@albertyeung5787]

excellent