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I have the following function

$f(x,y) = \log_2 (aby - ab^2y + acy -2abcy +ab^2cy - ab^2 + ab^2x + b - bx - abc + ab^2c + abcx - ab^2cx)$

I wanted to find $(x,y)$ that maximizes this function. However, when I compute the first derivative, with respect to x and set it to 0, I get the following

$$\frac{\partial f}{\partial x} = \frac{ab^2 - b + abc - ab^2c}{aby - ab^2y + acy -2abcy +ab^2cy - ab^2 + ab^2x + b - bx - abc + ab^2c + abcx - ab^2cx} = 0$$

As you can see there's no $x$ nor $y$ in the numerator. How am I supposed to get the critical point in this case?

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  • $\begingroup$ The expression inside the log is linear in $x$ and $y$. What makes you think the extreme values occur at critical points? $\endgroup$
    – almagest
    Jan 27, 2020 at 19:14
  • $\begingroup$ Then how do you recommend finding the extreme value of the function? $\endgroup$
    – Bikas
    Jan 27, 2020 at 21:05

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