The area (in square metres) of a rectangular garden with perimeter can be written as

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

The area (in square metres) of a rectangular garden with perimeter

40\,\text{m}

can be written as

A(x)=x(20-x)

, where

x\,(0\le x\le20)

is the length of the garden. Find the value of

x

that gives the maximum area.