What is the extreme f(x,y)=-3(20x-400)^2-6/7 (2y-44)^2+8 ?

The extreme f(x,y)=-3(20x-400)^2-6/7 (2y-44)^2+8 is Maximum(20,22)

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extreme f(x,y)=-3(20x-400)^2-6/7 (2y-44)^2+8

extreme points

f (x, y) = - 3 (20 x - 400)^{2} - \frac{6}{7} (2 y - 44)^{2} + 8

Maximum (20, 22)

Solution steps

Find the critical points:

(20, 22)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{48}{7}

D (x, y) = \frac{115200}{7}

Check the sign of at each critical point

Check critical point

(20, 22) :

Maximum

Maximum (20, 22)

f (x) = x - 8 3 x

f (x) = 2 x^{3} - 15 x^{2} + 36 x + 10

f (x) = (2 x - 1) e^{- x^{2}}

f (x) = x^{3} - 12 x^{2} + 45 x + 5

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

What is the extreme f(x,y)=-3(20x-400)^2-6/7 (2y-44)^2+8 ?
The extreme f(x,y)=-3(20x-400)^2-6/7 (2y-44)^2+8 is Maximum(20,22)