Maximum area when x=

Question

A rectangle is constructed under the graph off(x) = with one corner at ( 6, 0) and one corner on the graph of f(x) =  (0≤x≤6).

Represent the area A of the rectangle as a 

function of x: A(x)=

What value of x will maximize the area of the 

rectangle? Maximum area when x=

Answer 1

The rectangle always has one side = to x²; the other side is 6-x.

A=(6-x)x²

dA/dx= 12x-3x².=0...exclude x= 0 and you get your answer!