Yani buys a certain brand of cereal that costs $10 per box. yani changes to a super-saving brand of the same size. the equation shows the price, y, as a function of the number of boxes, x, for the new brand. y = 7x part a: how many more $'s is the price of a box of yani's original brand of cereal than the price of a box of the super-saving cereal? show your work. part b: how much money does yani save each month with the change in cereal brand if he buys 5 cereal boxes each month? show your work.

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