What is the extreme f(x)=-(x^2)/8+(y^2)/(78.13)+8 ?

The extreme f(x)=-(x^2)/8+(y^2)/(78.13)+8 is Saddle(0,0)

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extreme f(x)=-(x^2)/8+(y^2)/(78.13)+8

extreme points

f (x) = - \frac{x ^{2}}{8} + \frac{y ^{2}}{78.13} + 8

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0.02559 \dots

D (x, y) = - 0.00639 \dots

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = - (x - 4)^{2} \cdot (x + 4)^{2}

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

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

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

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

What is the extreme f(x)=-(x^2)/8+(y^2)/(78.13)+8 ?
The extreme f(x)=-(x^2)/8+(y^2)/(78.13)+8 is Saddle(0,0)