Question

Consider the surface: \[x^2 + 2y^2 + 3xz = 10\]

Answer 1

What about this surface?

Answer 2

Ok, I'm considering it.

Answer 3

haha I wasn't done typing :)

Answer 4

Find the tangent plane to the surface at the point (1, 2,1/3).

Answer 5

part b:

Answer 6

I think you'd just want to use the gradient here?

Answer 7

so I take the partials?

Answer 8

Bears, yes, the gradient is defined as the vector of the partials, more of:
\[\Delta f=<\delta/\delta x,\delta/\delta y,\delta/\delta z>\]. You simply dot the partial with a vector <(x-1),(y-2),(z-(1/3)> and set it to zero. In other words:
\[\delta/\delta x=2x+3z\]
\[\delta/\delta y=4y\]
\[\delta/\delta z=3x\]
So the gradient then is <2x+3z,4y,3x>. Dot that with <(x-1),(y-2),(z-(1/3))> and set it to zero and you have your solution. :) Let me know if it doesn't work out

Answer 9

thank you, that cleared it up :)

Answer 10

You're welcome :)