The sum of two variable positive numbers is $200$. Let $x$ be one of the numbers and let the product of these two numbers be $y$. Find the maximum value of $y$.
NB: I'm currently on the stationary points of the calculus section of a text book. I can work this out in my head as $100 \times 100$ would give the maximum value of $y$. But I need help making this into an equation and differentiating it. Thanks!