- #1
Jenkz
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Homework Statement
Find the four stationary points of the function:
u(x, y) = 4x^3 − 18(x^2)y + 24x(y^2) − 120y
Determine whether they are maxima, minima or saddle points.
Homework Equations
To find stationary points use:
E= (d^2u/dxy)^2 - [(d^2u/dx^2) * (d^2u/dy^2)]
E>0 saddle
E < 0 Maximum -> d^2u/dx^2 < 0
Minimum -> d^2u/dx^2 > 0
The Attempt at a Solution
du/dx = 12x^2 - 36xy +24y^2 (1)
du/dy = -18x^2 + 48xy-120 (2)
Stationary points mean both du/dx and du/dy are equal to 0. Here I should find simultaneous solution of equations (1) and (2). This is where I get stuck and I am not sure how to find them.
I have done the next part though:
E= (-36x + 48y)^2 - (1152x^2 - 1728xy)
But I need the stationary points to find the min/max/saddle points.