1 results for Let Fxyexxey 1 find fx and fy2 Set them equal

1 results for Let F(x,y)=e^x-xe^y. 1. find fx and fy.2. Set them equal to zero and slove to find the critical point. 3. Find fxx,fyy,fxy and fyx and then use them to calculate d(x,y) . 4. what have you found? local maximum,local minimum or saddle point?

F(x,y) = e^x - xe^y

1,2) f_x = e^x - e^y = 0

x = y

f_y = -xe^y = 0

x = 0 => y = 0

(0, 0) is only critical point

3) f_xx = e^x

f_yy = -xe^y

f_xy = -e^y

f_yx = -e^y

4) D = f_xxf_yy - f_xyf_yx = -xe^x+y - e^2y

D(0,0) = -1 < 0

so (0,0) is a saddle point

1 results for Let F(x,y)=e^x-xe^y. 1. find fx and fy.2. Set them equal to zero and slove to find the critical point. 3. Find fxx,fyy,fxy and fyx and then use th

1 results for Let Fxyexxey 1 find fx and fy2 Set them equal

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