What is the extreme f(x*y)=xy+8^{xy} ?

The extreme f(x*y)=xy+8^{xy} is Saddle(0,0)

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extreme f(x*y)=xy+8^{xy}

extreme points

f (x \cdot y) = x y + 8^{x y}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 9 ln^{2} (2) \cdot 8^{x y} x^{2}

D (x, y) = - 9 ln^{2} (2) \cdot 2^{3 x y + 1} x y - 27 ln^{3} (2) \cdot 2^{6 x y + 1} x y - 9 ln^{2} (2) \cdot 6 4^{x y} - 3 ln (2) \cdot 2^{3 x y + 1} - 1

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = x^{2} - 6 x + 12

f (t) = \frac{x}{x + 25} [0.9]

f (x) = - x^{3} + 3 x^{2} + 429 x + 5242

f (t) = 108 t - t^{3}

f (x) = 2 x^{3} + 6 x^{2} - 90 x + 1, - 5 \leq x \leq 7

What is the extreme f(x*y)=xy+8^{xy} ?
The extreme f(x*y)=xy+8^{xy} is Saddle(0,0)