What is the extreme f(x,y)=4xy+120y-20y^2-1/10 x^2y-90 ?

The extreme f(x,y)=4xy+120y-20y^2-1/10 x^2y-90 is Maximum(20,4)

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extreme f(x,y)=4xy+120y-20y^2-1/10 x^2y-90

extreme points

f (x, y) = 4 x y + 120 y - 20 y^{2} - \frac{1}{10} x^{2} y - 90

Maximum (20, 4)

Solution steps

Find the critical points:

(20, 4)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 40

D (x, y) = 8 y - 16 + \frac{8 x}{5} - \frac{x ^{2}}{25}

Check the sign of at each critical point

Check critical point

(20, 4) :

Maximum

Maximum (20, 4)

f (x, y) = 2 x^{2} + 4 y^{2} - 2 x y - 10 x - 2 y + 2

f (x) = \frac{7 x}{x ^{2} + 9}, 0 \leq x \leq 9

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

f (x) = x \cdot (ln (x))^{5}

f (x, y) = 40000 x + 30000 y - 8 x^{2} - 15 y^{2} - 10 x y

What is the extreme f(x,y)=4xy+120y-20y^2-1/10 x^2y-90 ?
The extreme f(x,y)=4xy+120y-20y^2-1/10 x^2y-90 is Maximum(20,4)