1. ## profit maximization unconstrainted

I have the eq. f(x,y) = 2x^2 + x^2y + y^3 + 12y^2
trying to find the stationary points for this eq.
i have the p.derivatives at:
fx = 4x - 2xy
fy = x^2 + 3y^2 + 24y
fxx = 4 + 2y
fyy = 6y + 25
fxy = 2x

my issue lies is that i need to find the 4 stationary points

for fx i have factored out to reach fx=x(4 + 2y)
and for fy = x^2 + y(3y + 24)

from here i am unsure how i get my x and y points if someone could show me how to go from here it would be very helpful

2. Originally Posted by manichee
I have the eq. f(x,y) = 2x^2 + x^2y + y^3 + 12y^2
trying to find the stationary points for this eq.
i have the p.derivatives at:
fx = 4x - 2xy
fy = x^2 + 3y^2 + 24y
fxx = 4 + 2y
fyy = 6y + 25
fxy = 2x

my issue lies is that i need to find the 4 stationary points

for fx i have factored out to reach fx=x(4 + 2y)
and for fy = x^2 + y(3y + 24)

from here i am unsure how i get my x and y points if someone could show me how to go from here it would be very helpful

you have a typo: it's + instead - in $f_x$.

Now, we have $x(4+2y)=0 \Longleftrightarrow x=0\,\,or\,\,y=-2.$ Plug in these values in $f_y$ and find the possible values for y in each case.

Tonio

3. so i do thanks for picking that up wats the maths behind just saying x = 0 and y = -2? i know thats what i have to do but im not sure in the actual steps involved in getting there