What is the extreme f(4.6)=x^y ?

The extreme f(4.6)=x^y is Saddle(1,0)

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extreme f(4.6)=x^y

extreme points

f (4.6) = x^{y}

Saddle (1, 0)

Solution steps

Find the critical points:

(1, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = x^{y} ln^{2} (x)

D (x, y) = y^{2} x^{2 y - 2} ln^{2} (x) - y x^{2 y - 2} ln^{2} (x) - x^{2 (y - 1)} - 2 y x^{2 y - 2} ln (x) - y^{2} x^{2 (y - 1)} ln^{2} (x)

Check the sign of at each critical point

Check critical point

(1, 0) :

Saddle

Saddle (1, 0)

E (X, Y) = (X + Y)^{2} - 3 (X + Y) (X - Y)

x^{2} - 7 x + 13

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

f (x) = x^{3} - 6 x^{2} + 9 x - 7

f (x) = 2 x^{5} - x^{4} - 9 x^{3} + 13 x^{2} - 5 x