Let f(x) = e^-2x. For x > 0, let P(x) be the perimeter of the
rectangle with vertices (0, 0), (x, 0), (x, f(x)) and (0, f(x)).
Which of the following statements is true? 

(a) The function P has an absolute minimum but not an absolute maximum on the interval (0, ∞).
(b) The function P has an absolute maximum but not an absolute minimum on the interval (0, ∞).
(c) The function P has both an absolute minimum and an absolute maximum on the interval (0, ∞).
(d) The function P has neither an absolute maximum nor an absolute minimum on the interval (0, ∞), but the graph of the function P does have an inflection point with positive x-coordinate.
(e) The function P has neither an absolute maximum nor an absolute minimum on the interval (0, ∞), and the graph of the function P does not have an inflection point with positive x coordinate.