What is the extreme f(x,y)=-6x^2-y^2+9x-5y+8 ?

The extreme f(x,y)=-6x^2-y^2+9x-5y+8 is Maximum(3/4 ,-5/2)

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extreme f(x,y)=-6x^2-y^2+9x-5y+8

extreme points

f (x, y) = - 6 x^{2} - y^{2} + 9 x - 5 y + 8

Maximum (\frac{3}{4}, - \frac{5}{2})

Solution steps

Find the critical points:

(\frac{3}{4}, - \frac{5}{2})

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

D (x, y) = 24

Check the sign of at each critical point

Check critical point

(\frac{3}{4}, - \frac{5}{2}) :

Maximum

Maximum (\frac{3}{4}, - \frac{5}{2})

f (x) = x^{2} + \frac{240}{x}

f (x) = 6 x^{4} - 8 x^{3} - 24 x^{2} + 35

f (x) = x + \frac{13}{x}

f (x) = \frac{2 x}{x ^{2} + 9}

2 x^{3} - 4 x^{2} + 2 x + 1

What is the extreme f(x,y)=-6x^2-y^2+9x-5y+8 ?
The extreme f(x,y)=-6x^2-y^2+9x-5y+8 is Maximum(3/4 ,-5/2)