What is the extreme f(x,y)=e^{8x}-xy^3 ?

The extreme f(x,y)=e^{8x}-xy^3 is Saddle(0,2)

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extreme f(x,y)=e^{8x}-xy^3

extreme points

f (x, y) = e^{8 x} - x y^{3}

Saddle (0, 2)

Solution steps

Find the critical points:

(0, 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 6 x y

D (x, y) = - 384 e^{8 x} x y - 9 y^{4}

Check the sign of at each critical point

Check critical point

(0, 2) :

Saddle

Saddle (0, 2)

f (x y) = ln (4 - x - y)

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

f (x, y) = 3 x + y

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

4 x^{3} + 6 x + 2

What is the extreme f(x,y)=e^{8x}-xy^3 ?
The extreme f(x,y)=e^{8x}-xy^3 is Saddle(0,2)