Need assistance with how to achieve the critical points as lecture notes and lecture video are relatively vague.

(Relative Extrema of Function of Two Variables)

Find and classify the critical points of z = (x²-3x)(y²-7y)

Local maximums:

Local minimums:

Saddle Points:

For each classification, enter a list of ordered pairs (x,y) where the max/min/saddle occurs. If there are no points for a classification, enter DNE.

Zx= (2x-3)(y²-7y)Zy=(X²-3x)Zxy = (2x-3)(2y-7)

Zxx = 2(y²-7y)Zyy= 2(x²-3x)Zxy = (2x-3)(2y-7)

fx= (2x-3)(y²-7y) = (2x-3)(y)(y-7)=0

fy = (x²-3x)(2y-7) = x(x-3)(2y-7) = 0

1y(2x-3)(y-7)=0

1x(x-3)(2y-7)=0

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