Question

find the dimension of the rectangle wiht a perimeter of 100 m that has the largest possible area.

Answer 1

The maximum is \[A = l \times w\]
the constraint is \[2l + 2w = 100\]
in terms of x \[2x +2w = 100\]
\[2w = 100 - 2x\]
\[w = 50 - x\]
A = x(50-x)

Answer 2

A= 50x -x^2
end points (0, 50]
find the first derivative A' = 50 - 2x
set equal to zero x = 25

Answer 3

x = 0, A = 0
x =25, A = 625
x =50 A = 0

so what's my dimension?