Question

Use Lagrange's method to determine the critical points of
z = f(x,y) = 2x + 2y subject to x^2 + y^2 + z^2 = 9

Answer 1

soo partial derivative way no good?

Answer 2

It is:)

But this question was in my test this morning and specifically asked to use L's method... Help pls:| hah

Answer 3

ah well i dont know what lagrange is xD, i did see a video titles lagrange method on the MIT lecture site, u want link?

Answer 4

That would help a lot, thanks!

Answer 5

u cud also try to find the gradient equation and see where its normal is pointed in K direction only

Answer 6

ok gimme sec

Answer 7

http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-13-lagrange-multipliers/

Answer 8

Thanks a lot!

Answer 9

u r welcome :)

Answer 10

While I entirely trust the effectiveness of MIT's video lectures (I've used them from time to time!), I just want to include one other thing I find myself often referring to when I see Lagrange Multipliers on OpenStudy (since despite going over the method every time, it still eludes me when I find it again, such as now!)

>> http://tutorial.math.lamar.edu/Classes/CalcIII/LagrangeMultipliers.aspx

Answer 11

I'm interested in this method, could you please put the final solution here so I can check if I did it right? Thanx!

Answer 12

F =2x + 2y - z, G = L(x^2 + y^2 + z^2 - 9)

Fx =2, Gx = L 2x
Fy =2, Gy = L 2y
Fz = -1, Gz = L 2z

equating the F and G parts

x = 1/L
y = 1/L
z = -2/L

solve for L in the restraint

x^2 + y^2 + z^2 = 9

1/L^2 + 1/L^2 + 4/L^2 = 9

5/L^2 = 9

5/9 = L^2

L = +- sqrt(5)/3