What is the extreme f(x)=-5x^2-8y^2-2xy+102y ?

The extreme f(x)=-5x^2-8y^2-2xy+102y is Maximum(-17/13 , 85/13)

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extreme f(x)=-5x^2-8y^2-2xy+102y

extreme points

f (x) = - 5 x^{2} - 8 y^{2} - 2 x y + 102 y

Maximum (- \frac{17}{13}, \frac{85}{13})

Solution steps

Find the critical points:

(- \frac{17}{13}, \frac{85}{13})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 16

D (x, y) = 156

Check the sign of at each critical point

Check critical point

(- \frac{17}{13}, \frac{85}{13}) :

Maximum

Maximum (- \frac{17}{13}, \frac{85}{13})

f (x) = x^{\frac{2}{3}}, - 1 \leq x \leq 8

2 x^{3} - 3 x^{2} - 72 x + 1

f (x) = \frac{x ^{5}}{5} - ln (x)

f (x, y) = 8 x^{4} - x^{2} + 3 y^{2}

What is the extreme f(x)=-5x^2-8y^2-2xy+102y ?
The extreme f(x)=-5x^2-8y^2-2xy+102y is Maximum(-17/13 , 85/13)