What is the extreme f(x,y)=6x-8y+7xy ?

The extreme f(x,y)=6x-8y+7xy is Saddle(8/7 ,-6/7)

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extreme f(x,y)=6x-8y+7xy

extreme points

f (x, y) = 6 x - 8 y + 7 x y

Saddle (\frac{8}{7}, - \frac{6}{7})

Solution steps

Find the critical points:

(\frac{8}{7}, - \frac{6}{7})

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 49

Check the sign of at each critical point

Check critical point

(\frac{8}{7}, - \frac{6}{7}) :

Saddle

Saddle (\frac{8}{7}, - \frac{6}{7})

f (x) = - x^{3} + 3 x^{2} - 9

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

f (x, y) = 5 x^{2} y^{3} + 4 x^{2} + 5 y

f (x) = 4 x^{3} - 36 x^{2} + 6

f (x) = x^{2} + y^{2} - 14 x + 12 y - 13

What is the extreme f(x,y)=6x-8y+7xy ?
The extreme f(x,y)=6x-8y+7xy is Saddle(8/7 ,-6/7)