Question 1. Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation

8p^3+x^2=65,600.

Determine the rate at which sales are changing at a time when

x=40,

p=20,

and the price is falling at the rate of

$.10 per week.

The rate at which sales are changing is

(Blank) per week

Question 2. Let

P(t)

be the price of a certain stock at time t during a particular day. When the stock reaches its highest price during the day, are

P(t)

and

P(t)

positive or negative? Explain your answer.

Question 3. The profit function (in millions) for a beverage company for the years

2008 through 2016 can be approximated by f(x)=28x^2+784x2915, where x=8 corresponds to the year 2008.

(a) During what year did a local maximum profit occur?

(b) What was the maximum profit?