I'm trying to find the minimum and maximum values of

on the surface of

I have already put

Getting the following 4 equations... Where do I go from here?

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- May 26th 2010, 04:55 PMkeysar7LaGrange Multiplier Problem
I'm trying to find the minimum and maximum values of

on the surface of

I have already put

Getting the following 4 equations... Where do I go from here?

- May 26th 2010, 05:15 PMpickslides
- May 26th 2010, 05:19 PMkeysar7I know I need to solve...
There are 4 unknowns (counting

**λ**) but variables x, y, z are raised to the power of 4.

I don't know how to solve this system... Any help? - May 26th 2010, 05:33 PMpickslides

Do this for the next 2 equations

Then becomes

Your work will replace and with a function of

You will then have a solution for and use this to find - May 27th 2010, 02:17 AMHallsofIvy
Since the value of is not part of the solution, I often find it best to eliminate first by

**dividing**one equation by another.

Dividing the first equation by the second gives or so .

Dividing the third equation by the second gives so .

Putting x= -2y and z= -3y into the last equation gives a single equation for y.