# Calculus - maximizing area

We first formulate everything in mathematical terms: if $x$ is the distance from the origin of one lower corner of the rectangle, then the base of the rectangle is $2x$, and the height of the rectangle is $10-x^2$. Its area is therefore
$A=2x\cdot(10-x^2).$
To maximize $A$, we remember that $A$ is differentiable everywhere and approaches $0$ at the boundary points of its domain, and therefore that $A$ will attain an extremum at some point at which $\frac{dA}{dx}=0$.