Math Is Fun Forum

sarsalan

Member

Registered: 2008-11-03

Posts: 16

Extrema of multi variable functions.

Q 3. If f(x,y) = x^3/3+4/3y^3-x^2-3x-4y-3
Find relative extrema and saddle points of f.

sarsalan

Member

Registered: 2008-11-03

Posts: 16

Re: Extrema of multi variable functions.

Q 3. If f(x,y) = x^3/3+4/3y^3-x^2-3x-4y-3
Find relative extrema and saddle points of f.

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Extrema of multi variable functions.

To find relative extrema and saddle points you need to find the partial derivatives Fx and Fy. Set Fx and Fy equal to zero and find the values of x and y that make the partial derivatives equal to zero, which will give you the critical points of the surface.

Now that you have your critical points you can apply this test:

If D > 0 and Fxx > 0 then f has a min at the critical point.
If D > 0 and Fxx < 0 then f has a max at the critical point.
If D < 0 then it is a saddle point.
If D = 0 then you cannot make any conclusions.