(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant 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

3. 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.

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# Homework Help: Stationary Points

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