Hi, I'm in the midst of revision for a calculus exam next week. I'm not sure if I tackled this problem correctly.
Find the maximum and minimum distances from the origin for points on the curve described by
3x^2 + 2y^2 + z^2 = 20 and z^2 = 2xy .
I know the constraint eqns defined by g(x,y,z)= 3x^2 + 2y^2 + z^2 - 20 = 0 and h(x,y,z)= z^2 = 2xy
Also I define the function f(x,y,z)= x^2 + y^2 + z^2, which I have to find the minimum and maximum values for.
In short, what I did was to introduce a function F(x,y,z,k,j) = f(x,y,z) - k[g(x,y,z)] - j[h(x,y,z)] and solve for grad(F)=0 ( k and j are constants)
The problem is when I realised 1 of the constants I had used turns out to be 0, is that correct?
PLEASE, would really appreciate some guidance on this: my ans is minimum: (-sqrt(13/8), 0, 0) and max: (sqrt(13/8), 0, 0)
Will be really glad if I can countercheck with some of your answers