Solve an Ellipse Product Min Problem with LaGrange

[MatSci]

Hello, the problem that i can't figure out says: To Use LaGrange multipliers to find all points on the ellipse 8x^2 + 2y^2 = 16 at which the product xy is a minimum? Any hints appreciated.

 

[Hurkyl]

What have you done so far?

 

[MatSci]

I'm just not sure what the "which the XY product is a minimum" is really asking me.

 

[Hurkyl]

xy is your objective function, the one you're trying to minimize.

 

[WillP]

to have a minimum of a function the 1st derivative must equal 0 and the second derivative must be greater than 0.

does that help?

 

[MatSci]

ah ok, and my ellipse is the constraint then?

 

[Hurkyl]

Looks that way.