Tangent Plane

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by stephaniejoy19
Last updated 6 years ago

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Tangent Plane

Don't just memorize it...understand it!

Finding the Tangent Plane

Remember the Point-Slope Formula?In case you need a refresher, here it is:y – yo = m(x – xo)Now, this formula only works for lines. Generalized so that it can be used to find a tangent line to any curve, it looks like this:y – f(xo) = f’(xo)(x – xo)It is VERY similar, I know!Now we are simply increasing by one dimension – instead of a tangent line, we are finding a tangent plane, and instead of two total variables, now we are dealing with three total variables – so our formula looks like this: z – f(xo, yo) = fx(xo, yo)(x – xo) + fy(xo, yo)(y – yo)

See? We're just expanding ideas from algebra!

Here's a picture of what one looks like.

In the video, her method may look a little different, but she is really doing it the same way! She just names components of the given point with x1 and y1 instead of xo and yo. Also, her given point has three components instead of two – she is given z1 so she doesn’t have to find z1 = f(x1, y1). Other than that, it’s the same!


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