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

The extreme f(x)=e^{-x+y}+x+2y^2 is Minimum(-1/4 ,-1/4)

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

extreme points

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

Minimum (- \frac{1}{4}, - \frac{1}{4})

Solution steps

Find the critical points:

(- \frac{1}{4}, - \frac{1}{4})

\frac{\partial ^{2} f}{\partial x ^{2}} = 4 + e^{y - x}

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

Check the sign of at each critical point

Check critical point

(- \frac{1}{4}, - \frac{1}{4}) :

Minimum

Minimum (- \frac{1}{4}, - \frac{1}{4})

f (x, y) = x^{2} y + y^{3} - 12 y

f (x) = 4 z^{3} - 3 z^{2} + 9 z + 12

f (x, y) = (4 x + 2 y, - x + y, 0)

g (x, y) = ln (x + y)

f (x, y) = - 4 x^{2} - 6 y^{2} - 4 x y + 800 x + 900 y - 10000

What is the extreme f(x)=e^{-x+y}+x+2y^2 ?
The extreme f(x)=e^{-x+y}+x+2y^2 is Minimum(-1/4 ,-1/4)