Originally Posted by

**ramdrop** hey im pretty stuck with this, I've got quite far though, I think..

f(x,y) =$\displaystyle 1/3x^3 + 1/3y^3 - 4xy^2 +15y$

then df/dx = $\displaystyle x^2 - 4y^2$

df/dy = $\displaystyle y^2 - 8xy + 15$

Then to find the stationary points, we must equate the differentials to 0, and I get to the 4 points:

(2y, -15), (2y, 8x+15), (-2y, -15), (-2y,8x+15)

Then by using the Hessian matrix

H = fxx fxy

fyx fyy

Where fxx = 2x, fyy = 2y - 8x, fyx = -8, fxy = 8y

Then the determinant is $\displaystyle 4xy - 16x^2 + 64y$

Then you put in the x and y co-ordinates and determine whether is a maxima or minima as < or > 0.

But I don't have any numbers...so if anybody can help or see where I've gone wrong

Thanks