Question

A builder has 2400 feed of barrier and wants to barricade off a rectangular ground that borderlands a straight water flow. No barrier is required along the entire length of the water flow.

Find the dimension of the ground that has the largest area

Answer 1

The graphic picture of such a situation is presented above. The point is to find such 0 < x < 1200 that x*(2400-2x) is maximized

$f(x)=2400x-2x^2\implies f'(x)=2400-4x$

The critical points $f'(x)=0\implies 2400-4x=0\implies x=600$

f(x) is a qudratic function with negative coefficient of $x^2$, so the critical point is the point of maximum, which means the sought dimensions is 600 and 1200