Find the local maximum and minimum values and saddle point(s) of the function. F

Question

Find the local maximum and minimum values and saddle point(s) of the function.
Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x, y) = 3(x^2+y^2)e^(y^2 - x^2)

local maximum value(s)=
local minimum value(s)=0

saddle point(s) (x, y, f)=

Explanation / Answer

df/dx = 6xe^(y^2 - x^2) + 3(x^2+y^2)(-2x)e^(y^2 - x^2) = 6(x - x^3 - xy^2) e^(y^2 - x^2) df/dy = 6ye^(y^2 - x^2) + 3(x^2+y^2)(2y)e^(y^2 - x^2) = 6(y+ x^2 y + y^3) e^(y^2 - x^2) for extremum, df/dx = df/dy = 0 x = x(x^2+y^2) y = -y(x^2+y^2) this is achieved at x=y=0. thus minimum = 3*0*1 = 0

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