MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
The marginal profit, in dollars per unit, for producing a certain item is modeled by M(p)=−4p+20, where p is the selling price per unit in dollars. Which statement best describes how the total profit changes as the price increases from 3 to 7?
(a) Profit decreases throughout this price range because M(p) is negative for all p between 3 and 7.
(b) Profit increases until the price reaches 5 and decreases thereafter.
(c) Profit decreases until the price reaches 5 and increases thereafter.
(d) Profit increases throughout this price range because M(p) is positive for all p between 3 and 7.