,DOWNLOAD THE Test Bank for Calculus Single and Multivariable 7th
Edition Hughes-Hallett
1. For any number r, let m(r) be the slope of the graph of the function y = (2.3) x at the point
x = r. Estimate m(4) to 2 decimal places.
Ans: 23.31
difficulty: medium section: 2.1
2. If x(V ) = V 1/ 3 is the length of the side of a cube in terms of its volume, V, calculate the
average rate of change of x with respect to V over the interval 3 < V < 4 to 2 decimal
places.
Ans: 0.15
difficulty: easy section: 2.1
3. The length, x, of the side of a cube with volume V is given by x(V ) = V 1/ 3 . Is the
average rate of change of x with respect to V increasing or decreasing as the volume V
decreases?
Ans: increasing
difficulty: medium section: 2.1
Page 1
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,DOWNLOAD THE Test Bank for Calculus Single and Multivariable 7th
Edition Hughes-Hallett
Chapter 2: Key Concept: The Derivative
4. If the graph of y = f(x) is shown below, arrange the following in ascending order with 1
representing the smallest value and 6 the largest.
A. f '( A) B. f '( B) C. f '(C ) D. slope of AB
E. 1 F. 0
Part A: 6
Part B: 3
Part C: 2
Part D: 4
Part E: 5
Part F: 1
difficulty: medium section: 2.1
5. The height of an object in feet above the ground is given in the following table.
Compute the average velocity over the interval 1 ≤ t ≤ 3.
t (sec) 0 1 2 3 4 5 6
y (feet) 10 45 70 85 90 85 70
Ans: 20
difficulty: easy section: 2.1
Page 2
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, DOWNLOAD THE Test Bank for Calculus Single and Multivariable 7th
Edition Hughes-Hallett
Chapter 2: Key Concept: The Derivative
6. The height of an object in feet above the ground is given in the following table. If
heights of the object are cut in half, how does the average velocity change, over a given
interval?
t (sec) 0 1 2 3 4 5 6
y (feet) 10 45 70 85 90 85 70
A) It is cut in half. C) It remains the same.
B) It is doubled. D) It depends on the interval.
Ans: A difficulty: medium section: 2.1
7. The height of an object in feet above the ground is given in the following table, y = f (t ) .
Make a graph of f (t ) . On your graph , what does the average velocity over a the
interval 0 ≤ t ≤ 3 represent?
t (sec) 0 1 2 3 4 5 6
y (feet) 10 45 70 85 90 85 70
A) The average height between f(0) and f(3).
B) The slope of the line between the points (0, f(0)), and (3, f(3)).
C) The average of the slopes of the tangent lines to the points (0, f(0)), and (3, f(3)).
D) The distance between the points (0, f(0)), and (3, f(3)).
Ans: B difficulty: medium section: 2.1
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Edition Hughes-Hallett
1. For any number r, let m(r) be the slope of the graph of the function y = (2.3) x at the point
x = r. Estimate m(4) to 2 decimal places.
Ans: 23.31
difficulty: medium section: 2.1
2. If x(V ) = V 1/ 3 is the length of the side of a cube in terms of its volume, V, calculate the
average rate of change of x with respect to V over the interval 3 < V < 4 to 2 decimal
places.
Ans: 0.15
difficulty: easy section: 2.1
3. The length, x, of the side of a cube with volume V is given by x(V ) = V 1/ 3 . Is the
average rate of change of x with respect to V increasing or decreasing as the volume V
decreases?
Ans: increasing
difficulty: medium section: 2.1
Page 1
mynursytest.store
,DOWNLOAD THE Test Bank for Calculus Single and Multivariable 7th
Edition Hughes-Hallett
Chapter 2: Key Concept: The Derivative
4. If the graph of y = f(x) is shown below, arrange the following in ascending order with 1
representing the smallest value and 6 the largest.
A. f '( A) B. f '( B) C. f '(C ) D. slope of AB
E. 1 F. 0
Part A: 6
Part B: 3
Part C: 2
Part D: 4
Part E: 5
Part F: 1
difficulty: medium section: 2.1
5. The height of an object in feet above the ground is given in the following table.
Compute the average velocity over the interval 1 ≤ t ≤ 3.
t (sec) 0 1 2 3 4 5 6
y (feet) 10 45 70 85 90 85 70
Ans: 20
difficulty: easy section: 2.1
Page 2
mynursytest.store
, DOWNLOAD THE Test Bank for Calculus Single and Multivariable 7th
Edition Hughes-Hallett
Chapter 2: Key Concept: The Derivative
6. The height of an object in feet above the ground is given in the following table. If
heights of the object are cut in half, how does the average velocity change, over a given
interval?
t (sec) 0 1 2 3 4 5 6
y (feet) 10 45 70 85 90 85 70
A) It is cut in half. C) It remains the same.
B) It is doubled. D) It depends on the interval.
Ans: A difficulty: medium section: 2.1
7. The height of an object in feet above the ground is given in the following table, y = f (t ) .
Make a graph of f (t ) . On your graph , what does the average velocity over a the
interval 0 ≤ t ≤ 3 represent?
t (sec) 0 1 2 3 4 5 6
y (feet) 10 45 70 85 90 85 70
A) The average height between f(0) and f(3).
B) The slope of the line between the points (0, f(0)), and (3, f(3)).
C) The average of the slopes of the tangent lines to the points (0, f(0)), and (3, f(3)).
D) The distance between the points (0, f(0)), and (3, f(3)).
Ans: B difficulty: medium section: 2.1
Page 3
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