Computing a tangent plane

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Here you can see how to use the control over functions whose graphs are planes, as introduced in the last video, to find the tangent plane to a function graph.

[@haroldh6678]

This is such a great video. After watching this I was able to solve all my equations right away with more understanding. Keep up the great work man, the visual representations played such a key role.

[@eladmenahem2253]

so true

[@savagepinksock]

i wondered why you were talking so fast then i realised i had it on double speed :/

[@MrBadermiy]

teaches better than my uni

[@tylergeorge7818]

ong

[@TheAmunik]

This video saved me so much time, thank you!!!

[@tylergeorge7818]

thank you great video, finals tomorrow... one of the last things I had to figure out.

[@S24W2]

Thank you so much Grant, much appreciated

[@SomeRandomFellow]

you sound just like 3Blue1Brown

[@luffyorama]

He IS the same guy lol

[@SomeRandomFellow]

Ahmad Max really? I KNEW IT

[@shawon265]

@@SomeRandomFellow really? That's a joke? Man, you gotta work on those

[@pedroafonso8384]

@@shawon265 he might have legitimately been surprised in that comment, we may never know the true interpretation :)

[@atriagotler]

8:30 that sound grant made😂👏

[@Anonymous-rj2lk]

ooTooTooTooT!

[@MrGarkin]

ye, lets call variable a y_not, y not.

[@fubukishirou6950]

Awesome video sir... thank you

[@preetphool]

simply awesome

[@gnikola2013]

When you are so into maths it ends up consuming all of the remaining neurons you had 8:32

[@huan320]

Omg how good is it,,,,,,,

[@arsalansyed4709]

Thank you so much! Without you I would hate math!

[@angelgarciamath]

What happens if the chosen point x does not belong to the surface? How do you find the tangent surface in that case and how does that look in comparison with the one in the video?

[@HanOnkel]

Well, if it's not on the surface, it's not a tangent point, is it?

[@samirkhan6195]

The point on surface through which you wanna find a tangent plane, Is automatically on the tangent plane.

[@Otto-cz6by]

Can you find dz/dx and dz/dy and then use the cross product to find the equation of the plane?

[@That_One_Guy...]

There's 2 redundant things from your solution
1. Why would you need normal vector when you can just directly use the partial derivatives to get the plane equation
2. Cross product is redundant here as soon as you find out the derivatives, because you can easily found the normal vector components (which is the coefficient of standard form) by moving all the x and y along with their coefficient to the left side and leaving only the constant in the right side

[@Otto-cz6by]

@@That_One_Guy... yeah, well when I wrote that, I just did the exam, but didn't study that section, all I knew was that partial derivatives were when all the other derivatives were zero. So I just put dx/dy in the vector, and 1 and 0 for the direction. It seemed correct mathematically, but I wasn't sure.

[@WorldWideSk8boarding]

what was the video before this?

[@evanparshall1323]

It seems like this only works with convex functions. Is that correct?

[@samirkhan6195]

At a point on the surface, if looking from one direction the surface looks convex, then looking from the opposite direction it will look concave.

[@wardtenhaaf558]

8:32 hahahhaha

[@WorldWideSk8boarding]

Why wouldnt the tangent planes equation be 0=a(x-x0)+b(y-y0)+c(z-z0) where a,b,c are the partial derivative of the surface evaluated at x0,y0,z0 ???

[@vgtboy]

I think what you stated above is equivalent to the equation in the video. z is L(x,y). Partial derivative for z is not needed as f is the same as z :). It is the value we're looking for
1. The plane should pass through x0, y0, z0
2. At x0, y0, z0, the plane should be tangential to f(x,y). That's why we need the partial dervatives at x0 and y0 to match for both plane and f(x,y)
We're then calculating for a function/'z' value that satisfies the need for a plane at these conditions. c would basically be dz/dz, which is 1. Plug that in and it should resemble the form of the equation in the video.

[@WorldWideSk8boarding]

@@vgtboy thanks for detailed explanation it actually makes perfect sense! I finished the course already but i really enjoyed it, math is cool 😎 shouldve been a math major.

[@vgtboy]

@@WorldWideSk8boarding No problem, glad you found it helpful. I'm still just learning haha. Are there any other resources you found helpful along the way to learning multivariable calculus? (channels , websites, etc). I'm trying to build a base for ML if possible

[@siddharthamondal4346]

Is this Grant Sanderson of 3b1b?????????

[@swaree]

He is