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82 Chapter 2: Differentiation
2.1 The Derivative and the Tangent Line Problem
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the slope of the line tangent to the graph of the function at the
point .
a.
b.
c.
d.
e.
____ 2. Find the slope of the line tangent to the graph of the function at the
point .
a.
b.
c.
d.
e.
____ 3. Find the derivative of the function by the limit process.
a.
b.
c.
d.
e.
____ 4. Find the derivative of the function by the limit process.
a.
b.
c.
d.
e.
2.1 The Derivative and the Tangent Line Problem 83
____ 5. Find the derivative of the following function using the limiting
process.
a.
b.
c.
d.
e.
____ 6. Find the derivative of the following function using the limiting process.
a. –4
b.
c.
d.
e.
____ 7. Find the derivative of the following function using the limiting process.
a.
b.
c.
d.
e.
____ 8. Find the derivative of the following function using the limiting process.
a.
b.
c.
d.
e.
84 Chapter 2: Differentiation
____ 9. Find the derivative of the following function using the limiting process.
a.
b.
c.
d.
e.
____ 10. Find the derivative of the function using the limiting process.
a.
b.
c.
d.
e.
____ 11. Find the derivative of the function by the limit process.
a.
b.
c.
d.
e.
2.1 The Derivative and the Tangent Line Problem 85
____ 12. Find an equation of the tangent line to the graph of the function at
the point .
a.
b.
c.
d.
e.
____ 13. Find an equation of the tangent line to the graph of the function at the
point .
a.
b.
c.
d.
e.
____ 14. Find an equation of the line that is tangent to the graph of the function and
parallel to the line .
a.
b.
c.
d.
e.
____ 15. Find an equation of the line that is tangent to the graph of and parallel to the given
line.
a.
b.
c. and
d.
e. and
86 Chapter 2: Differentiation
____ 16. Find an equation of the line that is tangent to the graph of the function
and parallel to the line .
a.
b.
c.
d.
e.
____ 17. The graph of the function f is given below. Select the graph of .
a. d.
2.1 The Derivative and the Tangent Line Problem 87
b. e.
c.
____ 18. Identify the graph which has the following characteristics.
Graph 1 Graph 2
88 Chapter 2: Differentiation
Graph 3 Graph 4
a. Graph 2
b. Graph 3
c. Graph 1
d. Graph 4
e. none of the above
____ 19. Use the alternative form of the derivative to find the derivative of the function
at .
a.
b.
c.
d.
e.
____ 20. Use the alternative form of the derivative to find the derivative of the function
at .
a.
b.
c.
d.
e.
2.1 The Derivative and the Tangent Line Problem 89
____ 21. Describe the x-values at which the graph of the function given below
is differentiable.
a. is differentiable at .
b. is differentiable everywhere except at .
c. is differentiable everywhere except at .
d. is differentiable on the interval .
e. is differentiable on the interval .
90 Chapter 2: Differentiation
2.1 The Derivative and the Tangent Line Problem
Answer Section
2.1 The Derivative and the Tangent Line Problem 91
