that at least one of the values, A, B, C would be greater than D at every value of x and y

Looks like he is saying A or B or C is always greater in that interval.

]]>A is out, it is not always greater than D in the closed interval (0,1).

B is out, it is not always greater than D in the closed interval (0,1).

C is out, it is not always greater than D in the closed interval (0,1).

]]>D surface is always below at least one other

I am not following you here. Please post the exact question. Wording is very important in mathematics.

]]>A = 9xy

B = 9x + 9y - 18xy

C = 9 - 9x - 9y + 9xy

D = 12xy - 6x - 6y + 6

I want to prove that there are no values of x and y (where x and y are both values between 0 and 1) for which D is the greatest.

Is that possible to do numerically? Only thing i can think of is having some software plot a 3d graph and show that the D surface is always below at least one other - obviously thats no good for helping me do my homework though lol.

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