What is the extreme f(x,y)=e^{10x^2+4y^2+2} ?

The extreme f(x,y)=e^{10x^2+4y^2+2} is Minimum(0,0)

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extreme f(x,y)=e^{10x^2+4y^2+2}

extreme points

f (x, y) = e^{10 x^{2} + 4 y^{2} + 2}

Minimum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 8 (8 e^{10 x^{2} + 4 y^{2} + 2} y^{2} + e^{10 x^{2} + 4 y^{2} + 2})

D (x, y) = 160 (20 e^{10 x^{2} + 4 y^{2} + 2} x^{2} + e^{10 x^{2} + 4 y^{2} + 2}) (8 e^{10 x^{2} + 4 y^{2} + 2} y^{2} + e^{10 x^{2} + 4 y^{2} + 2}) - 25600 e^{2 (10 x^{2} + 4 y^{2} + 2)} x^{2} y^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Minimum (0, 0)

f (x) = ln (x^{2} + 3 x + 8)

f (x) = 9 sin (3 x)

f (x, y) = 16 - 8 x + 10 y

f (x) = 20 sin (2 x)

x (3 - x)

What is the extreme f(x,y)=e^{10x^2+4y^2+2} ?
The extreme f(x,y)=e^{10x^2+4y^2+2} is Minimum(0,0)