1) The hypotenuse of a right triangle has one corner at the origin and one corner 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?
2) Use the Intermediate Value Theorem and Rolle's Theorem to show that the equation has exactly one solution: x^3 + e^x = 0