Definition amount: f (x, y)=xye^(? ((x?a)^2)? ((y?b)^ 2))

[problem1]

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?

 

[Deleted member 4993]

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?

Hint:

Use gradient and normal vector definitions.

Then show your work - indicating exactly where you are stuck.