Stationary points

1. The problem statement, all variables and given/known data

Find the stationary point(s) and also find out whether the stationary point(s) are minimum/maximum

z = 2x + 5y - 5y² - 5x² - 4xy - 1000



2. Relevant equations



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3. The attempt at a solution

I'm not 100% sure if I was correct and laid the answer out properly, can someone please help me check it out and correct any mistakes



fx = 2 - 10x - 4y

fy = 5 - 10y - 4x

fxx = -10

fyy = -10

fxy = -4



2 - 10x - 4y = 0, therefore 4y = 2 and y = 0.5

Possible stationary points (0,0.5) (0,-0.5)



5 - 10y - 4x = 0, therefore 4x = 5 and x = 1.2

Possible stationary points (0,0.5) (0,-0.5)

(1.25,0) (-1.25,0)



fxxfyy-f²xy = 84 (Greater than 0, and fxx & fyy are less than 0 therefore it's a maximum)