Lagrange Multipliers (Multivariable Calc)

[aznduk]

Homework Statement

Find the maximum x1, x2, x3, in the ellipsoid
x1^2/a^2 + x2^2/b^2 + x3^2/c^2 < 1 and all the places where this value is attained.

Homework Equations

The Attempt at a Solution

My teacher said to use the lagrange multiplier.
So far, I have that we are maximizing x1, x2, and x3 such that x1^2/a^2 + x2^2/b^2 + x3^2/c^2 < 1.

In any case, I figured that the constraint would be the equation for the ellipsoid, but I haven't a clue what exactly we would be maximizing for.
I would assume the maximum of x1,x2, and x3 would simply be the norm of the vector created by the three values.

 

[siddharth]

You need to show your work before you get help. What have you done with this problem?

 

[aznduk]

yeah I added what I did, but I feel like I'm going in the wrong direction.

 

[HallsofIvy]

Homework Statement

Find the maximum x1, x2, x3, in the ellipsoid
x1^2/a^2 + x2^2/b^2 + x3^2/c^2 < 1

Homework Equations

The Attempt at a Solution

My teacher said to use the lagrange multiplier.
So far, I have that we are maximizing x1, x2, and x3 such that x1^2/a^2 + x2^2/b^2 + x3^2/c^2 < 1.

In any case, I figured that the constraint would be the equation for the ellipsoid, but I haven't a clue what exactly we would be maximizing for.
I would assume the maximum of x1,x2, and x3 would simply be the norm of the vector created by the three values.

I wouldn't. I accept exactly what was said here: that you are asked to find three separate values: the maximum value of x, the maximum value of y, and the maximum value of z- and you don't need "Lagrange multiplier", you can read them off the equation of the ellipsoid. If you think your teacher means anything else, you should ask him or her.