Question

Alice has 20 cm of wire. She makes a rectangular shape with the
wire. The shape has the largest possible area. What is the length and
width of the shape ALice made? Explain how you worked it out.

Answer 1

$2x+2y=20\:\;->\;\;y=10-x\\ S=xy=x(10-x)\\ \frac{dS}{dx}=10-2x\\ \frac{dS}{dx}=0\;\;->\;\;x=5,\;\;y=10-x=5.\\ Point\;(5,5)\;is\ the\ maximum\ point\ because\;\;\frac{d^2S}{dx^2}=-2<0$