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

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

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

extreme points

P (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^{3} - \frac{9}{2} x^{2} + 1

y = 2 x^{2} + z^{2}

f (x, y) = 1 - 3 x^{4} - 6 x^{2} y + 2 y^{3}

f (x) = 8 x^{3} + 13 x

f (x, y) = 18 y^{2} + x^{2} - x^{2} y

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