# cal3

posted by .

Find and classify all local minima, local maxima, and saddle points of the function f(x,y)= -3yx^2-3xy^2+36xy

• cal3 -

F = -3yx^2-3xy^2+36xy
Fx = -6xy - 3y^2 + 36y
Fxx = -6y

Fy = -3x^2 - 6xy + 36x
Fyy = -6x

Fxy = -6x - 6y + 36

D = FxxFyy-(Fxy)^2 = 36xy - 36(x+y-6)^2

Fx = 0 Fy=0 at (0,0)
D<0 so a saddle point

Fx = -6xy - 3y^2 + 36y
Fx = 0 when y = 2(6-x)

Fy = -3x^2 - 6xy + 36x
Fy = 0 when x = 2(6-y)

So there is a local max for z along those two lines

• cal3 -

Okay Im just confused as how to get Fx=0 and Fy=0, If I set -6xy-3y^2+36y=0 how do i solve this?? Algebra was so long ago!
could you detail that part of the problem...

## Similar Questions

1. ### How to sketch graph of...

a differentiable function y =f(x) that has the given properties. 1. local minimum at (1,1), and local maximum at (3,3) 2. local minima at (1,1) and (3,3) 3. local maxima at (1,1) and (3,3) I don't remember how to do this. Thank you. …
2. ### how to sketch a graph of..

Local minimum and local maximum imply that the function approaches negative and positive infinite at opposite sides of the graph. Local minimum (1,1) and local maximum (3,3) means the slope of the function is 0 at these points. Thank …
3. ### college algebra

Let f(x)= x^5/120 - x^3/6 + x Find the local minima and maxima, then determine where the function is decreasing and increasing. Basically, I just need to know how to type this correctly in my calculator so I can get the right minima …
4. ### calculus

find and classify all local minima, local maxima, and saddle points of the function f(x,y)= e^-y(x^2+y^2)
5. ### cal3

Find and classify all local minima, local maxima, and saddle points of the function f(x,y)= -3yx^2-3xy^2+36xy I really need help answering this one!! Please answer in detail! Thank you
6. ### cal3/algebra help me!

Find and classify all local minima, local maxima, and saddle points of the function f(x,y)= -3yx^2-3xy^2+36xy I really need help answering this one!! Please answer in detail! Thank you This is what I have so far... D=FxxFyy-(Fxy)^2=(-6y)(-6x)-(-6x-6y+36)^2 …
7. ### Calculus Find max and min and saddle

Find and classify all local min and maxima and saddle points of the function f(x,y)=/3yx^2-3xy^2+36xy I know there are 3 saddle points and one maxima. This is what I got: D=FxxFyy-(Fxy)^2 = 36xy-36(x+y-6)^2 But how do i solve for zero?