What is the extreme f(x,y)=e^{5x^2+5y^2+3} ?

The extreme f(x,y)=e^{5x^2+5y^2+3} is Minimum(0,0)

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extreme f(x,y)=e^{5x^2+5y^2+3}

extreme points

f (x, y) = e^{5 x^{2} + 5 y^{2} + 3}

Minimum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 10 (10 e^{5 x^{2} + 5 y^{2} + 3} y^{2} + e^{5 x^{2} + 5 y^{2} + 3})

D (x, y) = 100 (10 e^{5 x^{2} + 5 y^{2} + 3} x^{2} + e^{5 x^{2} + 5 y^{2} + 3}) (10 e^{5 x^{2} + 5 y^{2} + 3} y^{2} + e^{5 x^{2} + 5 y^{2} + 3}) - 10000 e^{2 (5 x^{2} + 5 y^{2} + 3)} x^{2} y^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Minimum (0, 0)

f (x) = - 2 x^{3} + 42 x^{2} - 240 x + 5

y = 6 x - x^{2} - 2

f (x) = \frac{1}{( x ^{2} - 2 x + 7 )}

f (x) = 3 x^{2} - 27

x^{2} - 14 x + 3

What is the extreme f(x,y)=e^{5x^2+5y^2+3} ?
The extreme f(x,y)=e^{5x^2+5y^2+3} is Minimum(0,0)