Optimization and Modeling
The hypotenuse of a right triangle has one end at the origin and one end on the curve y = (x^2)*e^(-3x), with x > 0. One of the other two sides is on the x-axis, the other side is parallel to the y-axis. Find the maximum area of such a triangle. At what x-value does it occur?
All right, I know that I'll probably need A = (1/2)bh. I know I have to in some way find out where the curve intersects either the vertical side of the triangle or the hypotenuse to maximize the area? I think? But I don't know if i'm thinking the right way, and I don't know how to go about setting this up.