Exam 2: Rate of Change: the Derivative

The following table gives the wind chill factor ( ) as a function of the wind speed (miles/hour) when the air temperature is 20 . What are the units for the derivative of wind chill with respect to wind speed when the air temperature is 20 ?

The following table gives the number of passenger cars, in millions, in the United States, C, as a function of years, t. We have . Estimate . Use the nearest right-hand value to make your estimate.

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 rate of change in the amount of lumber, in board-feet per inch, with respect to the radius when the radius is 21 inches?

Let . Derive an exact formula for the derivative function by computing algebraically the limit of a difference quotient.

The graph of a cost function is given in the following figure. Which item costs the most to produce?

Using the graph of , at x=C is positive ?

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

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

The function is graphed below. A. Is positive, negative, or zero? B. Is positive, negative, or zero?

A company graphs , the derivative of the number of pints of ice cream sold over the past ten years. Out of t=1,2,4,8, and 10, in what year was C ''(t) greatest?

The graph of in the figure gives the position of a particle at time t. Arrange the following values in order from smallest to largest by placing a "1" by the smallest, a "2" by the next smallest, and so forth. A. average velocity on . B. average velocity on . C. instantaneous velocity at t=1. D. instantaneous velocity at t=3. E. instantaneous velocity at t=10.

From the following graph, estimate .

There is a population of thousand bacteria in a culture at time t hours after the beginning of an experiment. You know that , , and . Using these values, make a prediction for

The graph of is shown in the following figure. Arrange the following values in order from smallest to largest by placing a "1" by the smallest, a "2" by the next smallest, and so forth. A. B. C. D. E.

The graph of is shown below. Arrange the following values in order from smallest to largest by placing a "1" by the smallest, a "2" by the next smallest, and so forth. A. B. C. D. slope AB E. 1 F. 0

Suppose a function is given by the following table of values. Is most likely positive or negative at x=1.9?

To produce 250 items the total cost is $4600 and the marginal cost is $11. Estimate the cost of producing 500 items.

Using a calculator, estimate the derivative of at x = . Make sure your calculator is set to radians.

Consider the two functions shown below. A. B.

Cost and revenue functions for a certain chemical manufacturer are given in the following figure. To maximize profit, how many tons should the company produce?