What is the critical f(x,y)=(5x+7y+25)e^{-(x^2+xy+y^2)} ?

The critical f(x,y)=(5x+7y+25)e^{-(x^2+xy+y^2)} is

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critical f(x,y)=(5x+7y+25)e^{-(x^2+xy+y^2)}

critical points

f (x, y) = (5 x + 7 y + 25) e^{- (x^{2} + x y + y^{2})}

- \frac{- 7 + \frac{72576}{169} + \frac{625 136048896}{24336}}{20}, - \frac{10800 + 136048896}{7488}, - \frac{19 136048896 + 169200 + 7488 \frac{2388933}{1352} + \frac{1925 136048896}{21632}}{149760}, \frac{136048896 - 10800}{7488}, \frac{- 169200 - 19 136048896 + 7488 \frac{2388933}{1352} + \frac{1925 136048896}{21632}}{149760}, \frac{136048896 - 10800}{7488}

Solution steps

(5 x + 7 y + 25) e^{- (x^{2} + x y + y^{2})}

Find where

\nabla f (x, y)

is equal to zero or undefined

- \frac{- 7 + \frac{72576}{169} + \frac{625 136048896}{24336}}{20}, - \frac{10800 + 136048896}{7488}, - \frac{19 136048896 + 169200 + 7488 \frac{2388933}{1352} + \frac{1925 136048896}{21632}}{149760}, \frac{136048896 - 10800}{7488}, \frac{- 169200 - 19 136048896 + 7488 \frac{2388933}{1352} + \frac{1925 136048896}{21632}}{149760}, \frac{136048896 - 10800}{7488}

x^{3} - 3 x^{2} + 2

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

f (x) = x^{3} + 4 x^{2} + 5 x - 2

3 x^{2} y + y^{3} - 3 x^{2} - 3 y^{2} + 2

f (x, y) = 4 x^{2} + 4 y^{2} - 4 x - 8 y

What is the critical f(x,y)=(5x+7y+25)e^{-(x^2+xy+y^2)} ?
The critical f(x,y)=(5x+7y+25)e^{-(x^2+xy+y^2)} is