Exam 2: Rate of Change: the Derivative

Consider the two functions shown below. A. B.

Estimate the value of using the following table. Use the nearest right-hand value to make your estimate.

Let be the temperature in degrees Celsius at a height h (in meters) above the surface of the earth. Which of the following gives the temperature in degrees Celsius at a height of 1000 meters?

The following table gives the wind chill factor ( ) as a function of the wind speed (miles/hour) when the air temperature is 20 . What is the derivative of wind chill with respect to wind speed when the air temperature is 20 and the wind speed is 20 miles per hour? Use the nearest right-hand value to make your estimate.

Given the following data about the function, f, use estimates of and to estimate . Use the nearest right-hand value to make your 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 .

Let . What is the change in between t=2 and t=5?

Suppose is the height in inches of a person who is t years old. Is it reasonable that ?

Suppose a function is given by the following table of values. Estimate the instantaneous rate of change of f at x=1.7, and use this estimate to find the equation for the tangent line to f at x=1.7. The line is y = _____x+_____. Use the nearest right-hand value to make your estimate.

The following table gives the number of passenger cars, in millions, in the United States, C, as a function of years, t. We have . Is f ''(t) positive or negative?

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

There is a function used by statisticians, called the error function, which is written y=erf(x). Suppose you have a statistical calculator, which has a button for this function. Playing with your calculator, you discover the following: Using this information alone, give an estimate for erf '(0), accurate to 2 decimal places.

The following figure is the graph of , the cumulative number of customers served in a certain store during business hours one day, as a function of the hour of the day. About when was the store the busiest?

A driver obeys the speed limit as she travels past different towns in the order A, B, C. In town A, the speed limit is 35 mph. In town B, the speed limit is 60 mph, and in town C the speed limit is 55 mph. It always takes her two minutes to reach the new speed limit when she passes by a new town. If represents the driver's position at time t, then is for the first two minutes she is passing town B positive or negative?

Write the Leibniz notation for the first and second derivatives of the given function and include units. "The amount of paint, G, in gallons, is a function of time m, in minutes"

The function is graphed below. Which is larger, or ?

At a production level of 2000 for a product, marginal revenue is $3.50 per unit and marginal cost is $3.00 per unit. Do you expect maximum profit to occur at a production level above or below 2000?

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

Let be the time, in minutes, that it takes for an oven to heat up to F. What are the units of ?

Let be the temperature in degrees Celsius at a height h (in meters) above the surface of the earth. Which of the following gives the rate of change of temperature with respect to a height at 70 meters above the surface of the earth, in degrees per meter?