What is the extreme f(x,y)=4y^2+5x^2-9y+8x-19 ?

The extreme f(x,y)=4y^2+5x^2-9y+8x-19 is Minimum(-4/5 , 9/8)

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extreme f(x,y)=4y^2+5x^2-9y+8x-19

extreme points

f (x, y) = 4 y^{2} + 5 x^{2} - 9 y + 8 x - 19

Minimum (- \frac{4}{5}, \frac{9}{8})

Solution steps

Find the critical points:

(- \frac{4}{5}, \frac{9}{8})

\frac{\partial ^{2} f}{\partial x ^{2}} = 8

D (x, y) = 80

Check the sign of at each critical point

Check critical point

(- \frac{4}{5}, \frac{9}{8}) :

Minimum

Minimum (- \frac{4}{5}, \frac{9}{8})

f (x) = 8 x^{2} + 8 x y + 10 y^{2} - 24 x - 28 y + 27

f (x) = x - 4 ln (x)

\frac{d}{d x} (\frac{x y}{x ^{2} - 1})

f (x) = x^{3} + 3 x^{2} - 45 x + 4

f (x, y) = - 6 x + 5 y

What is the extreme f(x,y)=4y^2+5x^2-9y+8x-19 ?
The extreme f(x,y)=4y^2+5x^2-9y+8x-19 is Minimum(-4/5 , 9/8)