What is the extreme x^3-48xy+64y^3 ?

The extreme x^3-48xy+64y^3 is Saddle(0,0),Minimum(4,1)

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extreme x^3-48xy+64y^3

extreme points

x^{3} - 48 x y + 64 y^{3}

Saddle (0, 0), Minimum (4, 1)

Solution steps

Find the critical points:

(0, 0), (4, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 384 y

D (x, y) = 2304 x y - 2304

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(4, 1) :

Minimum

Saddle (0, 0), Minimum (4, 1)

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

f (x) = e^{x} - 7 e^{- x} - 8 x

e^{- x^{2}} - 2 e^{- x^{2}} x^{2}

f (x) = x^{11} - 3 x^{9} + 2

f (x, y) = - 2.8 + x^{2} - 6.4 x y + 1.4 y^{2}

What is the extreme x^3-48xy+64y^3 ?
The extreme x^3-48xy+64y^3 is Saddle(0,0),Minimum(4,1)