Question

Find the tangent plane given the surface z=3(x-1)^2+2(y+3)^2+ 7 at the point (2,-2,12)

Answer 1

well we will definitely need the gradient at that point in order to construct a plane, so have you got that yet?

Answer 2

umm i dont think i need any gradient point this is a simple enough problem I just think I am doing the partial derrivative wrong

Answer 3

for the derrivative i got dz/dx=6x-6 and for dz/dy i got 4y+12

Answer 4

Those partials are right, but what are you planning on doing with them?

Answer 5

ok cool thanks. Well from there I will plug in the point to those partials. then use the formula for a tangent plane. the plane i got is z=6x+4y+8 :)

Answer 6

oh, you have a formula handy?
I was going to go through the whole process, lol

Answer 7

let me see if I get the same answer as you just for kicks

Answer 8

thatd be great

Answer 9

erm, I got a different answer
let me double-check...

Answer 10

oh yeah, I just messed up earlier, you're right
I think the gradient way is easier than remembering some specific formula, but take your choice

Answer 11

cool thanks