Question

Find the linearization of the function f(x,y)=sqrt(34−x^2−2y^2) at the point (-1, 2).

Answer 1

I got Z = x/10 + 4y/5 + 35/10 as my answer, where did I go wrong?

Answer 2

tried again, got z = x/10 - 4y/5 + 67/10...
Still wrong...

Any ideas Robtobey?

Answer 3

you guys here?

Answer 4

first f(-1,2) = 5
now
f(x,y) = f(-1,2) + fx(-1,2)(x-(-1)) + fy(-1,2)(y-2)

Answer 5

so fx = (1/2)[(34−x^2−2y^2)^(-1/2)] * (-2x) = -x * (34−x^2−2y^2)^(-1/2)
so fx(-1,2) = 0.2

Answer 6

how did I get my fx(-1,2) to be .1?

Answer 7

you ask me ? :P

Answer 8

that answer you gave didn't work, also :(

Answer 9

yes i have an error

Answer 10

fy = (1/2)[(34−x^2−2y^2)^(-1/2)] *(-4y) = -2y * (34−x^2−2y^2)^(-1/2)
fy(-1,2) = -4 * 0.2 = -0.8

so finally

f(x,y) = 5 + 0.2(x+1)-0.8(y-2)
f(x,y) = 0.2x -0.8y + 6.8

Answer 11

fixed here .. i deleted the wrong

Answer 12

hmm Thanks, I'll compare your work to mine to see that arithmatic I fluttered up. thanks again man.

Answer 13

the last one is good right ?

Answer 14

yes :)

Answer 15

ok :)