What is the extreme f(x,y)=(x-1)4+y^4+64(x-1)y+14 ?

The extreme f(x,y)=(x-1)4+y^4+64(x-1)y+14 is Saddle(65537/65536 ,-1/16)

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extreme f(x,y)=(x-1)4+y^4+64(x-1)y+14

extreme points

f (x, y) = (x - 1) 4 + y^{4} + 64 (x - 1) y + 14

Saddle (\frac{65537}{65536}, - \frac{1}{16})

Solution steps

Find the critical points:

(\frac{65537}{65536}, - \frac{1}{16})

\frac{\partial ^{2} f}{\partial x ^{2}} = 12 y^{2}

D (x, y) = - 4096

Check the sign of at each critical point

Check critical point

(\frac{65537}{65536}, - \frac{1}{16}) :

Saddle

Saddle (\frac{65537}{65536}, - \frac{1}{16})

f (x) = \frac{5}{( x - 5 ) ^{2}}

y = \frac{x ^{3}}{3} + 4 x^{2} + 15 x + 7

x^{2} - 3 x - 4

f (x) = e^{x} ln (x) y

f (x) = 2 x - 4 x - 7

What is the extreme f(x,y)=(x-1)4+y^4+64(x-1)y+14 ?
The extreme f(x,y)=(x-1)4+y^4+64(x-1)y+14 is Saddle(65537/65536 ,-1/16)