- #1
mintygreen
- 5
- 0
Find an equation of the largest sphere that passes through the point (-1,1,4) and is such that each of the points (x,y,z) inside the sphere satisfies the condition
x^2 + y^2 + z^2 < 136 + 2(x + 2y + 3z)
I know this problem requires Lagrange multipliers. I assume that x^2 + y^2 + z^2 is the f(x,y,z) that I want to maximize and I think that 2x + 4y + 6z = -136 is my g(x,y,z)=k? Beyond that, I can't figure out how to work with the inequality or incorporate the sphere passing through the points... Thanks for any help!
x^2 + y^2 + z^2 < 136 + 2(x + 2y + 3z)
I know this problem requires Lagrange multipliers. I assume that x^2 + y^2 + z^2 is the f(x,y,z) that I want to maximize and I think that 2x + 4y + 6z = -136 is my g(x,y,z)=k? Beyond that, I can't figure out how to work with the inequality or incorporate the sphere passing through the points... Thanks for any help!