Find the area A of the largest rectangle that can be inscribed under the curve of the equation below in the first and second quadrants. $$y = e^{-x^2}$$
Graph of the equation.
I don't know where to start. The book says look at chapter 5.4 but there is no example like this at all.
Best Answer
HINT: Clearly the top corners of the rectangle should both lie on the curve, so the corners of the rectangle will be at $\langle x,0\rangle$, $\langle x,e^{-x^2}\rangle$, $\langle -x,0\rangle$, and $\langle -x,e^{-(-x)^2}\rangle$ for some $a>0$. Write down a formula for the area of that rectangle as a function of $x$, and use the usual techniques to find where that function has its maximum.