Henry is starting a t-shirt printing business and plans on selling each shirt for $30, with his cost being $8 per shirt. The equipment will cost $1200. Henry orders 600 shirts and determines that the profit for his new business is modeled by the function p = 22x - 1200. What is the range of this function in this context? A) {0 ≤ p ≤ 500}
B) {0 ≥ p ≥ 500}
C) {-1,200 ≤ p ≤ 2,000}
D) {-1,200 ≤ p ≤ 12,000}

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0