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Exam 2: Rate of Change: the Derivative

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Exam 1: Functions and Change204 Questionsadd course
Exam 2: Rate of Change: the Derivative132 Questionsadd course
Exam 3: Shortcuts to Differentiation178 Questionsadd course
Exam 4: Using the Derivative94 Questionsadd course
Exam 5: Accumulated Change: the Definite Integral93 Questionsadd course
Exam 6: Antiderivatives and Applications122 Questionsadd course
Exam 7: Probability68 Questionsadd course
Exam 8: Functions of Several Variables134 Questionsadd course
Exam 9: Mathematical Modeling Using Differential Equations121 Questionsadd course
Exam 10: Geometric Series65 Questionsadd course
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To study traffic flow along a major road, the city installs a device at the edge of the road at 4:00 am. The device counts the cars driving past, and records the total periodically. The resulting data is plotted on a graph, with time (in hours) on the horizontal axis and the number of cars on the vertical axis. The graph is shown below. It is a graph of the function To study traffic flow along a major road, the city installs a device at the edge of the road at 4:00 am. The device counts the cars driving past, and records the total periodically. The resulting data is plotted on a graph, with time (in hours) on the horizontal axis and the number of cars on the vertical axis. The graph is shown below. It is a graph of the function = Total number of cars that have passed by after t hours. Estimate . = Total number of cars that have passed by after t hours. Estimate To study traffic flow along a major road, the city installs a device at the edge of the road at 4:00 am. The device counts the cars driving past, and records the total periodically. The resulting data is plotted on a graph, with time (in hours) on the horizontal axis and the number of cars on the vertical axis. The graph is shown below. It is a graph of the function = Total number of cars that have passed by after t hours. Estimate . . To study traffic flow along a major road, the city installs a device at the edge of the road at 4:00 am. The device counts the cars driving past, and records the total periodically. The resulting data is plotted on a graph, with time (in hours) on the horizontal axis and the number of cars on the vertical axis. The graph is shown below. It is a graph of the function = Total number of cars that have passed by after t hours. Estimate .

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Question 121

The following table gives the cost and revenue, in dollars, for different production levels, q. For what value of q is profit maximized? The following table gives the cost and revenue, in dollars, for different production levels, q. For what value of q is profit maximized?

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Question 122

Cost and revenue functions are graphed in the first figure. What does the second figure show? Cost and revenue functions are graphed in the first figure. What does the second figure show? Cost and revenue functions are graphed in the first figure. What does the second figure show?

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Question 123

Estimate Estimate when . Take smaller and smaller intervals until your estimate is accurate to 3 decimal places. when Estimate when . Take smaller and smaller intervals until your estimate is accurate to 3 decimal places. . Take smaller and smaller intervals until your estimate is accurate to 3 decimal places.

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Question 124

An amount of $500 was invested in 1970 and the investment grew as shown in the following table. (Amounts are given for the beginning of the year.) The average rate of increase of the investment between 1980 and 1990 is _____ per year. An amount of $500 was invested in 1970 and the investment grew as shown in the following table. (Amounts are given for the beginning of the year.) The average rate of increase of the investment between 1980 and 1990 is _____ per year.

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Question 125

Given the following data about the function f, estimate Given the following data about the function f, estimate . . Given the following data about the function f, estimate .

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Question 126

The graph below is the graph of The graph below is the graph of , the derivative of . At 2 is the original function M(x) increasing, decreasing, constant or undefined? , the derivative of The graph below is the graph of , the derivative of . At 2 is the original function M(x) increasing, decreasing, constant or undefined? . At 2 is the original function M(x) increasing, decreasing, constant or undefined? The graph below is the graph of , the derivative of . At 2 is the original function M(x) increasing, decreasing, constant or undefined?

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Question 127

The growth graph in the following figure shows the height in inches of a bean plant during 30 days. On the 15th day, the plant was growing about _____ inches/day. Round to 2 decimal places. The growth graph in the following figure shows the height in inches of a bean plant during 30 days. On the 15<sup>th</sup> day, the plant was growing about _____ inches/day. Round to 2 decimal places.

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Question 128

Consider the following graph. In region III, Consider the following graph. In region III, is ________ (positive/negative) and is ________ (positive/negative). is ________ (positive/negative) and Consider the following graph. In region III, is ________ (positive/negative) and is ________ (positive/negative). is ________ (positive/negative). Consider the following graph. In region III, is ________ (positive/negative) and is ________ (positive/negative).

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Question 129

The noise level, N, in decibels, of a rock concert is given by The noise level, N, in decibels, of a rock concert is given by , where d is the distance in meters from the concert speakers. Which of the following gives the distance, in meters, away from the speakers at which the noise is 80 decibels? , where d is the distance in meters from the concert speakers. Which of the following gives the distance, in meters, away from the speakers at which the noise is 80 decibels?

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Question 130

Let Let represent the dollar amount charged per hour by a computer consultant to a client when they sign a contract t hours of work. The consultant gives a discount to the client if the contract is increased by 10 hours. Interpret the following statements. A) . B) . represent the dollar amount charged per hour by a computer consultant to a client when they sign a contract t hours of work. The consultant gives a discount to the client if the contract is increased by 10 hours. Interpret the following statements. A) Let represent the dollar amount charged per hour by a computer consultant to a client when they sign a contract t hours of work. The consultant gives a discount to the client if the contract is increased by 10 hours. Interpret the following statements. A) . B) . . B) Let represent the dollar amount charged per hour by a computer consultant to a client when they sign a contract t hours of work. The consultant gives a discount to the client if the contract is increased by 10 hours. Interpret the following statements. A) . B) . .

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Question 131

Using a calculator, estimate the derivative of Using a calculator, estimate the derivative of at x = 0. Make sure your calculator is set to radians. at x = 0. Make sure your calculator is set to radians.

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Question 132
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