Question

just quickly,

if you were given a surface of the form z=f(x,y) ,

how would you find the co-ordinates of the point on the surface when you are given values for x and y?

Answer 1

Actually I am not sure whether the provided information is enough to give an answer. The way you give the surface z=f(x,y). What does that z mean? Is this a level-set equation or a height field or something else?

Answer 2

i'll attach the question?

Answer 3

Give it a try

Answer 4

we have previously calculated the partial derivitives of x and y.

Answer 5

Well, ok, but the pictures posted don't give any more information in that issue. What is your topic in school right now?

Answer 6

tangent planes

Answer 7

So as the answer I assume it just is (1, 2, f(1,2)). But I am not sure, because of the discussed problem.

Answer 8

i'll take a look.

Answer 9

genius! can you explain why though?

Answer 10

So a solution says it is correct?

Answer 11

yep

Answer 12

well, ok, then we most likely indeed have a height-field, so a scalar 2d function. If you have 2 dimensions for variables and a third one for the scalar itself, you have 3 dimensions alltogether. To describe a point in 3d you need 3 coordinates, which is the 1, the 2 and the f(1,2).
Illustrative the 1 and 2 stand for the coordinates on a map, the z=f(1,2) represents the height of the point (1,2), so meters over the sea (like 8000+x for the mount everest).

Answer 13

ohhhh, the height!

Answer 14

thanks alot! makes so much sense now!

Answer 15

You're welcome