 #1
Retro95
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Homework Statement
Find the stationary point(s) and also find out whether the stationary point(s) are minimum/maximum
z = 2x + 5y  5y^{2}  5x^{2}  4xy  1000
Homework Equations

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)
fxxfyyf^{2}xy = 84 (Greater than 0, and fxx & fyy are less than 0 therefore it's a maximum)