Solve Problem: Let f (x, y)=xye^(− ((x−a)^2)− ((y−b)^ 2))

[electricman]

Hi,

I have some problems to solve this:

Let f (x, y)=xye^(− ((x−a)^2)− ((y−b)^ 2)). In which direction, one will go from the point (a, b) in the definition amount if one wants to that the function values will increase so quickly as possible? Decide an equation for key planet to the surface z=f (x, y) in the point (a, b, ab). Use differential to f in order to calculate a close value to f (9a/10, 6b/5). In which points, key planet is to the surface z=f (x, y) horizontal?

Anyone who knows how to solve this?

 

[HallsofIvy]

Hi,

I have some problems to solve this:

Let f (x, y)=xye^(− ((x−a)^2)− ((y−b)^ 2)). In which direction, one will go from the point (a, b) in the definition amount if one wants to that the function values will increase so quickly as possible? Decide an equation for key planet to the surface z=f (x, y) in the point (a, b, ab). Use differential to f in order to calculate a close value to f (9a/10, 6b/5). In which points, key planet is to the surface z=f (x, y) horizontal?

Anyone who knows how to solve this?

Those are all basic 'grad f' problems. Do you know why? What is special about the direction grad f points. Please show SOME work if you expect help. Oh, and I think you mean "tangent plane" instead of "key planet".