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i need to find the mex and min point of the function f(x,y) = x^2*y*e^(-x^2 - 2y^2) for (x,y) in R^2

here is what i tried : i found the partial derivatives :

f_x = 2x*y*e^8-x^2 - 2y^2) + x^2*y*e^(-x^2 -2y^2)*(-2x)

and f_y = x^2*y*(-4y)*e^(-x^2 - 2y^2)

i see that those partials equals 0 in the point (0,0). is this the only stationary point here?

what is max / and what is minimum?

can anyone help me?

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# A max/min problem.

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