cal3
posted by Lucy .
Find and classify all local minima, local maxima, and saddle points of the function f(x,y)= 3yx^23xy^2+36xy

F = 3yx^23xy^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+y6)^2
Fx = 0 Fy=0 at (0,0)
D<0 so a saddle point
Fx = 6xy  3y^2 + 36y
Fx = 0 when y = 2(6x)
Fy = 3x^2  6xy + 36x
Fy = 0 when x = 2(6y)
So there is a local max for z along those two lines 
Okay Im just confused as how to get Fx=0 and Fy=0, If I set 6xy3y^2+36y=0 how do i solve this?? Algebra was so long ago!
could you detail that part of the problem...
Respond to this Question
Similar Questions

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. … 
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 … 
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 … 
calculus
find and classify all local minima, local maxima, and saddle points of the function f(x,y)= e^y(x^2+y^2) 
cal3
Find and classify all local minima, local maxima, and saddle points of the function f(x,y)= 3yx^23xy^2+36xy I really need help answering this one!! Please answer in detail! Thank you 
cal3/algebra help me!
Find and classify all local minima, local maxima, and saddle points of the function f(x,y)= 3yx^23xy^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)(6x6y+36)^2 … 
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^23xy^2+36xy I know there are 3 saddle points and one maxima. This is what I got: D=FxxFyy(Fxy)^2 = 36xy36(x+y6)^2 But how do i solve for zero? 
math about to have a test over this please help!
Unfortunately that is the entire problem.. Find and classify all local minima, local max, and saddle points of the function F(x,y)= 3x^2y3xy^2+36xy There should be 3 saddle points and a maxima for sure! Please help me get the points. … 
basic calculus
use the first and second derivatives to find the xcoordinates of all local maxima and minima of f(x)=8e^2x2x. indicate which of your answers are local minima and which are local maxima. 
calculus
Consider the function f(x) = e^sin(cos(x)) on the interval [0, 4π] a) The critical points of f are at__________?