Question

Bob has 20 feet of fencing to enclose a rectangular garden. If one side of the garden is x feet long, he wants the other side to be (10 – x) feet wide. What value of x will give the largest area, in square feet, for the garden?

Answer 1

The area of the fenced garden is \(A=x(10-x)=10x-x^2\).

Find the critical points of \(A(x)\) by solving for \(A'(x)=0\), then apply the first derivative test.