$A''(x) = -4 < 0$, so concave down → maximum.
Optimization problems are the “real reason” we learn calculus: to find the best (maximum profit, minimum cost, largest area, shortest time) given some constraint. 5.6 Solving Optimization Problems Homework
$y = 200 - 2(50) = 100$ ft.
$A'(x) = 200 - 4x$.
$200 - 4x = 0 \implies x = 50$ ft.