2. The profit function of a certain product is given by the function $P(x) = -x^3 + 9x^2 - 27x$, where $0 \le x \le 5$.
(a) Draw a sign chart for $P'(x)$ on the line below. Indicate values where $P'$ is 0, positive or negative.
(b) Give the intervals of increase and decrease of $P(x)$.
(c) Find the relative maxima and minima of $P(x)$ on the given interval, if any. If there aren't any, explain why.
(d) Find all absolute maxima and minima of $P(x)$ on the given interval.
(e) Give the intervals where $P(x)$ is concave up or down and determine if there are any inflection points.