Question

What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y=12-x^2?

Answer 1

Here's what we're working with:\[A=bh=(2x)(y)=2x(12-x^2)=A(x)\]Maximize the area A(x) by finding the roots of A'(x) and plugging them into the area formula. Discard negative answers obviously.