- #1

Roni1985

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## Homework Statement

"Find the equation of the plane that passes through the point (1,2,3) and cuts off the smallest volume in the first octant

There are many ways to solve it, I tried two of them and actually got the correct answer, but couldn't prove if this is the min or the max volume (I guess absolute min or max?)

## Homework Equations

for one attempt I used these equations:

a(x-1)+b(y-2)+c(z-3)=0

and

V=(1/3)*(A*h)

As far as the second method is concerned, I actually think this one is better and I used these two equations:

1/a+2/b+3/c=1 ( first had to find it)

V=(1/3)*(A*h)=(1/6)*(abc)

## The Attempt at a Solution

I used the Lagrange Multipliers to find a,b,c

This is what I got

b=6

a=3

c=9

Now I have a few questions:

1) if I used the first/second partial derivative tests to find local min or local max, how would you check the boarders here?

2) How do I prove that the point I found is an absolute minimum or an absolute maximum?

3) "cuts off the smallest volume" means that the volume of the tetrahedron has a minimum volume? or the compliment has a min value and then the volume of the tetrahedron has a max value ?

Thanks,

Roni.

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