MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
For a certain product, the daily cost C of production (in dollars) depends on the demand D (in units) according to
C(D)=500+20D.
The demand D depends on the selling price p (in dollars per unit) through the linear model
D(p)=1000−30p.
On a particular day, the selling price is p=18 and is decreasing at a rate of 0.10 dollar/week. All functions are differentiable.
(a) Determine the instantaneous rate of change of cost with respect to time, dtdC, at the moment when p=18. Express your answer in dollars per week, rounded to the nearest cent.
(b) Based on your result in part (a), state whether the cost of production is increasing or decreasing at that moment and justify your conclusion.