I already solved this but the detailed breakdown helps the general audience. but I am wondering about this now. Why did they say 4,0 is the max. I mean we know quadratic graphs but without doing dy/dx how did they know?\(\displaystyle y \ = \ \frac{4x}{1-2x} \ = \ \frac{4x\ - 2 \ + 2}{1-2x} \ = \ \frac{2(2x-1) \ + 2}{1-2x}\ =\ \frac{2 - 2(1-2x)}{1-2x}=\ 2 \cdot \ \frac{1 - (1-2x)}{1-2x}=\ (-2) \cdot \ \left[1 - \frac{1}{1-2x}\right]\)
Take time to do the algebra "correctly" - without that Calculus will be "far away"!