Lagrange Multipliers

[ctb94]

Hello,

I am having a bit of trouble with the Lagrange multiplier method. My question is:

Use the Lagrange multiplier method to find the extrema points of the distance from the point (1,2,3) to the surface of the sphere x²+y²+z²=4. Find the possible values for of λ.

This is what I have so far:

∇d=λq:


d(x,y,z)=(x-1)²+(y-2)²+(z-3)²

2(x-1)=λ2x
2(y-2)=λ2y
2(z-3)=λ2z

This is where I become stuck on the problem. Thank you in advance for any help with this problem!

 

[Ishuda]

Hello,

I am having a bit of trouble with the Lagrange multiplier method. My question is:

Use the Lagrange multiplier method to find the extrema points of the distance from the point (1,2,3) to the surface of the sphere x²+y²+z²=4. Find the possible values for of λ.

This is what I have so far:

∇d=λq:


d(x,y,z)=(x-1)²+(y-2)²+(z-3)²

2(x-1)=λ2x
2(y-2)=λ2y
2(z-3)=λ2z

This is where I become stuck on the problem. Thank you in advance for any help with this problem!

Solve the equations for x, y, and z in terms of \(\displaystyle \lambda\), put the x, y, and z point into the constraint equation to determine \(\displaystyle \lambda\) which, in turn, will determine x, y, and z/