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

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

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

extreme points

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

Minimum (- \frac{1}{2}, \frac{1}{4})

Solution steps

Find the critical points:

(- \frac{1}{2}, \frac{1}{4})

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

D (x, y) = 80

Check the sign of at each critical point

Check critical point

(- \frac{1}{2}, \frac{1}{4}) :

Minimum

Minimum (- \frac{1}{2}, \frac{1}{4})

f (x, y) = x^{2} + y^{2} - 10 x + 16 y - 6

f (x) = e^{- \frac{( x - 3 ) ^{2}}{2}} (- x + 3)

\frac{8 x ^{3}}{3} + 6 x^{2} - 8 x, - 3 \leq x \leq 1

f (x) = \frac{x ^{4}}{4} - (\frac{x}{3})^{3} - x^{2} + 1

f (x) = cos (x) - 9 x, 0 \leq x \leq 4 π

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