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

The extreme f(x,y)=e^{x^2+2y^2-5x-3y} is Minimum(5/2 , 3/4)

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

extreme points

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

Minimum (\frac{5}{2}, \frac{3}{4})

Solution steps

Find the critical points:

(\frac{5}{2}, \frac{3}{4})

\frac{\partial ^{2} f}{\partial x ^{2}} = e^{- 3 y + x^{2} + 2 y^{2} - 5 x} (16 y^{2} - 24 y + 13)

D (x, y) = e^{2 x^{2} - 10 x + 4 y^{2} - 6 y} (4 x^{2} - 20 x + 27) (16 y^{2} - 24 y + 13) - e^{2 (x^{2} + 2 y^{2} - 5 x - 3 y)} (2 x - 5)^{2} (4 y - 3)^{2}

Check the sign of at each critical point

Check critical point

(\frac{5}{2}, \frac{3}{4}) :

Minimum

Minimum (\frac{5}{2}, \frac{3}{4})

f (x) = x^{3} - 12 x^{2} + 45 x + 1

3 ∣ x ∣

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

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

f (x) = sec (x)

What is the extreme f(x,y)=e^{x^2+2y^2-5x-3y} ?
The extreme f(x,y)=e^{x^2+2y^2-5x-3y} is Minimum(5/2 , 3/4)