What is the extreme f(5/4 , 1/4)=2xy-x^2-5y^2+2x+1 ?

The extreme f(5/4 , 1/4)=2xy-x^2-5y^2+2x+1 is Maximum(5/4 , 1/4)

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extreme f(5/4 , 1/4)=2xy-x^2-5y^2+2x+1

extreme points

f (\frac{5}{4}, \frac{1}{4}) = 2 x y - x^{2} - 5 y^{2} + 2 x + 1

Maximum (\frac{5}{4}, \frac{1}{4})

Solution steps

Find the critical points:

(\frac{5}{4}, \frac{1}{4})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 10

D (x, y) = 16

Check the sign of at each critical point

Check critical point

(\frac{5}{4}, \frac{1}{4}) :

Maximum

Maximum (\frac{5}{4}, \frac{1}{4})

f (x) = 3 + x^{2} + x y + y^{2}

f (x) = 2 x + 2 y

f (x) = \frac{ln ( x )}{2 x}

f (x, y) = 23 - 2 x^{3} - y^{2} - 6 x y

2 x + \frac{1}{x}

What is the extreme f(5/4 , 1/4)=2xy-x^2-5y^2+2x+1 ?
The extreme f(5/4 , 1/4)=2xy-x^2-5y^2+2x+1 is Maximum(5/4 , 1/4)