# Rate of change

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Section 11.3

1) The quarterly profit of Cunningham Realty depends on the amount of money x spent on advertising/quarter according to the rule:

where and x are measured in thousands of dollars. What is Cunningham's profit when its quarterly advertising budget is $35,000.00?

2) Suppose the weekly supply and demand functions are given by:

respectively, where p is measured in dollars and x is measured in units of a thousand. Find the equilibrium quantity and price.

Section 11.6

3) Using the formula for the slope of a secant line passing through two points on a curve,

,

determine this secant line slope formula for the function . You must simplify your result algebraically.

4) Consider the graph of the function . Determine the slope of the secant line passing through the two points of the graph when and

Determine the equation of the line passing through the two points.

5) Use the four-step process outlined in the book (page 664)

Use the four-step process outlined in the book 4 step process: Compute

Form the difference

Form the quotient

Compute

to find the slope of a line tangent to the graph of the given function at any point.

6) Let

a) Find the average rate of change of the function with respect to x in the interval from to .

b) Find the derivative of f

c) Determine the instantaneous rate of change of the function when

d) Determine the instantaneous rate of change of the function when

7)

Let x and (x) represent the given quantities. Fix x=a and let h be a small positive number. Give an interpretation of the quantities

Note that you are asked to interpret the two different rates of change. You are to interpret the rates in terms of the names of the variables in the problem. Your solutions should include the appropriate units.

X denotes the speed of a car (in mph), and (x) denotes the fuel economy of the car measured in miles per gallon. mpg

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This provides several examples of working with rate of change as well as other calculus topics.