What is the extreme f(x,y)=e^{x^2+1}+e^{y^2+1} ?

The extreme f(x,y)=e^{x^2+1}+e^{y^2+1} is Minimum(0,0)

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extreme f(x,y)=e^{x^2+1}+e^{y^2+1}

extreme points

f (x, y) = e^{x^{2} + 1} + e^{y^{2} + 1}

Minimum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 2 (2 e^{y^{2} + 1} y^{2} + e^{y^{2} + 1})

D (x, y) = 4 (2 e^{x^{2} + 1} x^{2} + e^{x^{2} + 1}) (2 e^{y^{2} + 1} y^{2} + e^{y^{2} + 1})

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Minimum (0, 0)

f (x) = \frac{2 x ^{2} + 5}{x ^{2} - 25}

f (x, y) = x - 5 y + 6

f (x) = 2 x - 6 x^{\frac{1}{3}}

f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 11

f (x) = (1 + \frac{20}{x}) x^{2} + 144

What is the extreme f(x,y)=e^{x^2+1}+e^{y^2+1} ?
The extreme f(x,y)=e^{x^2+1}+e^{y^2+1} is Minimum(0,0)