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

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

Determine the largest area of the rectangle whose base is on the x-axis and two of its vertices lie on the curve $y=e^{-x^2}$.

The largest area of a rectangle which has one side on the $x-$axis and the two vertices on the curve $y=e^{-x^2}$ is

A rectangle has one side on the positive y-axis and one side on the positive x-axis. The upper right hand vertex on the curve $y=\frac{\ln x}{x^2}$. The maximum area of the rectangle is

A rectangle has one side on the positive $y$-axis and one side on the $x$-axis. The upper right hand vertex of the rectangle lies on the curve $y=\frac{\ell nx}{x^2}$ The maximum area of the rectangle is