Question

The length and width of a rectangle have a sum of 90. What dimensions give the maximum area?

Answer 1

Suppose the length is x, so the width is (90-x), so the area A=x(90-x)=90x-x^2
dA/dx = 90-2x. When dA/dx=0, x=45.
So 45x45 is the maximum area.

Answer 2

You can do second derivative dA^2/(dx)^2=-2<0, so this turning point is the maximum.

Answer 3

Thank you so much!! :D