Could someone please guide me through this problem? I\'ve done it twice now and

Question

Could someone please guide me through this problem? I've done it twice now and keep getting the question incorrect.

Find the critical points for the function f(x, y) = 4x2 - 8xy + 6y2 - 12y and classify each as a local maximum, local minimum, saddle point, or none of these. critical points: (give your points as a comma separated list of (x,y) coordinates.) classifications: (give your answers in a comma separated list, specifying maximum, minimum, saddle point, or none for each, in the same order as you entered your critical points)

Explanation / Answer

fx = 8x-8y=0

fy = -8x+12y -12=0

=>

solving gives (3,3) is the critical point

fxx = 8

fyy = 12

fxy = -8

D = fxxfyy-fxy^2 = 8*12 -64 = 32 >0

=>

it has a local minimum at (3,3)

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