What is the extreme f(x,y)=3x+5y-2x^2-3y^2 ?

The extreme f(x,y)=3x+5y-2x^2-3y^2 is Maximum(3/4 , 5/6)

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extreme f(x,y)=3x+5y-2x^2-3y^2

extreme points

f (x, y) = 3 x + 5 y - 2 x^{2} - 3 y^{2}

Maximum (\frac{3}{4}, \frac{5}{6})

Solution steps

Find the critical points:

(\frac{3}{4}, \frac{5}{6})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 6

D (x, y) = 24

Check the sign of at each critical point

Check critical point

(\frac{3}{4}, \frac{5}{6}) :

Maximum

Maximum (\frac{3}{4}, \frac{5}{6})

f (x, y) = x^{2} - 2 x + y^{2} + 2 y + 1

f (x) = 2 x + \frac{1}{x}

f (x) = e^{x^{2} - 3 x - 1}, - 3 \leq x \leq 3

f (x, y) = 4 - x^{2} + 9 - y^{2}

f (x, y) = (5 x + 7 y + 25) e^{- (x^{2} + x y + y^{2})}

What is the extreme f(x,y)=3x+5y-2x^2-3y^2 ?
The extreme f(x,y)=3x+5y-2x^2-3y^2 is Maximum(3/4 , 5/6)