Please explain your answer Find the absolute extrema of fx y

Please explain your answer

Find the absolute extrema of f(x, y) = x2 + 9y - 9xy on the region bounded by y = x, y = 0, and x = 4. f(4, 0) = 16 (absolute maximum); f(0, 0) = 0 (absolute minimum) f(4, 0) = 16 (absolute maximum); .f(4, 4) = -92 (absolute minimum) f(4, 4) = 92 (absolute maximum); f(0, 0) = 0 (absolute minimum) f(1, 2/9) (absolute maximum); f(4, 4) = -92 (absolute minimum)

Solution

first condition is y=x and x=4 mean f(4,4)
and second condition is x=4 and y=0 so f(4,0)
so only option contain both these limits is option 2.
So, without solving we can say that option 2 is correct.
but for your help i will solve the f(4,0) mean we will place x=4 and y=0

f(4,0)=16+0+0=16

f(4,4)=16+36-134=-92