Question: For a > 0, the following line forms a triangle in the first quadrant with the x- and y-axes:
a(a2 + 1)y = a - x
(a) In terms of a, find the x- and y-intercepts of the line.
(b) Find the area of the triangle, as a function of a.
(c) Find the value of a making the area a maximum.
(d) What is this greatest area?
(e) If you want the triangle to have area 1/5, what choices do you have for a?