The hypotenuse of a right triangle has one end at the origin and one end on the curve y(x) = X3e-5x, with x ≥0 . One of the other two sides is on the x-axis, the other side is parallel to the y-axis.
(a) Express the area of the triangle in terms of x only.
(b) Find A '(x)
(c) Find the critical point for x > 0.
(d) Find the maximum area of the triangle. Give an exact answer.