What is the extreme f(x,y)=-2x^2+8x-3y^2+24y+7 ?

The extreme f(x,y)=-2x^2+8x-3y^2+24y+7 is Maximum(2,4)

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extreme f(x,y)=-2x^2+8x-3y^2+24y+7

extreme points

f (x, y) = - 2 x^{2} + 8 x - 3 y^{2} + 24 y + 7

Maximum (2, 4)

Solution steps

Find the critical points:

(2, 4)

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

D (x, y) = 24

Check the sign of at each critical point

Check critical point

(2, 4) :

Maximum

Maximum (2, 4)

f (x) = x^{2} - 2 x + 2

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

f (x, y) = 400 - 64 x^{2} - 49 y^{2}

f (x) = (x^{2} - 5)^{4} (x^{2} + 1)^{5}

f (x) = 240 x + 57 x^{2} - x^{3}

What is the extreme f(x,y)=-2x^2+8x-3y^2+24y+7 ?
The extreme f(x,y)=-2x^2+8x-3y^2+24y+7 is Maximum(2,4)