What is the extreme f(x)=25x-25xe^{-y}-50y-x^2 ?

The extreme f(x)=25x-25xe^{-y}-50y-x^2 is Saddle(5/2 ,-ln(4/5)),Maximum(10,ln(5))

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extreme f(x)=25x-25xe^{-y}-50y-x^2

extreme

Saddle (\frac{5}{2}, - ln (\frac{4}{5})), Maximum (10, ln (5))

Solution steps

Find the critical points:

(\frac{5}{2}, - ln (\frac{4}{5})), (10, ln (5))

\frac{\partial ^{2} f}{\partial x ^{2}} = - 25 e^{- y} x

D (x, y) = 50 e^{- y} x - 625 e^{- 2 y}

Check the sign of at each critical point

Check critical point

(\frac{5}{2}, - ln (\frac{4}{5})) :

Saddle

Check critical point

(10, ln (5)) :

Maximum

Saddle (\frac{5}{2}, - ln (\frac{4}{5})), Maximum (10, ln (5))

What is the extreme f(x)=25x-25xe^{-y}-50y-x^2 ?
The extreme f(x)=25x-25xe^{-y}-50y-x^2 is Saddle(5/2 ,-ln(4/5)),Maximum(10,ln(5))