Math Is Fun Forum

Shelled

Member

Registered: 2014-04-15

Posts: 44

Lagrange multipliers

Hi, I'm having trouble with a few sections of the question below:

For the first part, I found the minimum points to be (+- sqrt(6),0,0) .
Since this point is contained just on the x-axis, would it be safe to assume that if I take the normal from this point, it too will have just an x component and as a result pass through the origin?

For the section about intersection in the yz plane:
I used distance as one of my functions (y^2 +z^2) and the given surface, yz=-6. I found my minimum value to be (0,- sqrt(6),sqrt(6)) and (0,sqrt(6), - sqrt(6)) using lagrange.
But I'm unsure how I'd use the values I've found to explain why it's not a minima on the 3D surface.

Any help would be appreciated

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Lagrange multipliers

Hi;

How did you use Lagrange on the first problem?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Shelled

Member

Registered: 2014-04-15

Posts: 44

Re: Lagrange multipliers

hi, I got the partial derivatives for f=x^2+y^2+z^2 (minimum distance from origin) and the given function, g=x^2-yz-6
so in terms of x: 2*x = 2*x*lambda (where lambda is the lagrange multiplier). I did the same for y and z.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Lagrange multipliers

Hi;

I found my minimum value to be (0,- sqrt(6),sqrt(6)) and (0,sqrt(6), - sqrt(6)) using lagrange.

I would use the distance formula on those two points with the origin. You would see that they are not a minimum.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Shelled

Member

Registered: 2014-04-15

Posts: 44

Re: Lagrange multipliers

Thank you I was a little lost as what to do with those points. I'll have a go at it

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Lagrange multipliers

Hi;

Let me know how you do.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.