Exam 2: Rate of Change: the Derivative

The graph of is shown in the following figure. Is positive, negative, or zero?

Assume that f and g are differentiable functions defined on all of the real line. If everywhere and everywhere then .

A. Give a difference quotient approximation (to one decimal place) of where . B. Find the equation of the line tangent to the graph of at the point where x = 3.

Given the graph below of , is positive, negative, zero or undefined?

Let be the length of the side of a cube in terms of its volume. As V decreases, does the rate of change of x increase or decrease?

The cost of extracting T tons of ore from a copper mine is dollars. Would you expect to be positive or negative?

Assume that f and g are differentiable functions defined on all of the real line. f can satisfy: everywhere, everywhere, and everywhere.

Given the following table, find MC(2).

Using a difference quotient, compute to 2 decimal places for .

In 2007, Apple's iTunes music store sold 2 billion songs. The number of iTunes songs purchased (in millions) is shown on the following chart, S(t), where time is measured in days since Apple iTunes sold 1 million songs (March 15, 2003). A) Estimate with the appropriate units. B) Use to estimate to 2 decimal places.

Consider the function f sketched in the following figure. Do you expect to be positive, negative, or zero?

Which point has a slope of -0.5 ?

Cost and revenue functions for a certain chemical manufacturer are given in the following figure. How much does it cost to produce 10 tons?

Approximate to 3 decimal places (with a difference quotient and a calculator) the derivative of at x = 1.

The distance that a bird flies is measured by y miles for x minutes, and is given by the function . What are the units of A) and B) ?

Assume that f and g are differentiable functions defined on all of the real line. It is possible that everywhere, everywhere, and everywhere.

Every day the Undergraduate Office of Admissions receives inquiries from eager high school students (e.g. "Please send me an application",etc.) They keep a running count of the number of inquiries received each day, along with the total number received until that point. Below is a table of weekly figures from about the end of August to about the end of October of a recent year. One of these columns can be interpreted as a rate of change. Which one is it?

Your friend Herman operates a neighborhood lemonade stand. . Last month he spent $2 and made 19 glasses of lemonade, and another time he spent $5 and made 83 glasses of lemonade. You decide to use this data to create a linear cost function, , giving the cost in dollars of making q glasses of lemonade. If lemonade sells for $0.15 per glass, how many glasses must he sell to break even?

Suppose the graph of f is in the figure below. Is positive, negative, or zero?

Let be the amount of lumber, in board-feet, produced from a tree of radius r (measured in inches). Which of the following gives the radius (in inches) of a tree that produces 150 board-feet of lumber ?