Brenda pours laundry detergent from a bottle into the cap and then into the washing machine. Every time she fills the cap, the amount of detergent in the bottle changes by -0.26 liters. She fills the cap 3 1/4 times in all. John has a different bottle of detergent that is the same size. Every time he fills his cap, the amount of detergent in his bottle changes by -0.21 liters. He fills his cap 2 5/6 times in all. Who has the greater total change in the amount of detergent in their bottle?

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