1. When you see…
Find the zeros
You think…

2. To find the zeros...

3. When you see…
Show that f(x) is even
You think…

4. Even function

5. When you see…
Show that f(x) is odd
You think…

6. Odd function

7. When you see…
Show that exists
You think…

8. Show exists
Show that

9. When you see…
You think…

10. Find Limit with calculator

11. When you see…
You think…

12. Find limits, no calculator

13. When you see…
You think…

14. Find limit with calculator

15. When you see…
You think…

16. Find limit, no calculator

17. Find horizontal asymptotes of f(x)
When you see…
Find horizontal asymptotes of f(x)
You think…

18. Find horizontal asymptotes of f(x)

19. When you see…
Find vertical
asymptotes of f(x)
You think…

20. Find vertical asymptotes of f(x)

21. When you see…
Find the domain
of f(x)
You think…

22. Find the domain of f(x)

23. Show that f(x) is continuous
When you see…
Show that f(x) is continuous
You think…

24. .f(x) is continuous

25. Find the slope of the tangent line to f(x) at x = a
When you see…
Find the slope of the tangent line to f(x) at x = a
You think…

26. Slope of tangent line

27. Find equation of the line tangent to f(x) at (a, b)
When you see…
Find equation of the line tangent to f(x) at (a, b)
You think…

28. Equation of the tangent line

29. Find equation of the line normal to f(x) at (a, b)
When you see…
Find equation of the line normal to f(x) at (a, b)
You think…

30. Equation of the normal line

31. Find the average rate of change of f(x) at [a, b]
When you see…
Find the average rate of change of f(x) at [a, b]
You think…

32. Average rate of change of f(x)
Find
f (b) - f ( a)
b - a

33. When you see…
You think…

34. Intermediate Value Theorem (IVT)

35. Find the interval where f(x) is increasing
When you see…
Find the interval where f(x) is increasing
You think…

36. f(x) increasing

37. Find the interval where the slope of f (x) is increasing
When you see…
Find the interval where the slope of f (x) is increasing
You think…

38. Slope of f (x) is increasing

39. Find the instantaneous rate of change of f(x)
When you see…
Find the instantaneous rate of change of f(x)
on [a, b]
You think…

40. Instantaneous rate of change of f(x)
Find f ‘ ( a)

41. Given s(t) (position function), find v(t)
When you see…
Given s(t) (position function), find v(t)
You think…

42. Given position s(t), find v(t)

43. Find f ’(x) by the limit definition
When you see…
Find f ’(x) by the limit definition
You think…

44. Find f ‘( x) by definition frequently asked backwards

45. Find the average velocity of a particle
When you see…
Find the average velocity of a particle
on [a, b]
You think…

46. Find the average rate of change on [a,b]

47. Given v(t), determine if a particle is speeding up at
When you see…
Given v(t), determine if a particle is speeding up at
t = k
You think…

48. Given v(t), determine if the particle is speeding up at t = k

49. Given a graph of find where f(x) is increasing When you see…
You think…

50. Given a graph of f ‘(x) , find where f(x) is increasing

51. When you see…
You think…

53. When you see…
You think…

54. Relative maximum

55. When you see…
You think…

56. Concave Down

57. When you see…
You think…

58. Points of Inflection

59. When you see…
Show that a piecewise function is differentiable at the point a where the function rule splits
You think…

60. Show a piecewise function is differentiable at x=a

61. When you see…
You think…

62. Derivative of Inverse Function

63. When you see…
You think…

64. Derivative of the inverse of f(x)

65. When you see…
You think…

66. Derivative Rules

67. When you see…
You think…

68. Implicit Differentiation

69. When you see…
Find the derivative of
f(g(x))
You think…

70. Chain Rule

71. Find the minimum value of a function
When you see…
Find the minimum value of a function
You think…

72. Minimum value of a function

73. Find the minimum slope of a function
When you see…
Find the minimum slope of a function
You think…

74. Minimum slope of a function

75. When you see…
Find critical numbers
You think…

76. Find critical numbers

77. Find the absolute maximum of f(x)
When you see…
Find the absolute maximum of f(x)
You think…

78. Find the absolute minimum of f(x)

79. When you see…
You think…

80. Rolle’s Theorem

81. When you see…
You think…

82. Mean Value Theorem

83. When you see…
Find the range
of f(x) on [a, b]
You think…

84. Find the range of f(x) on [a,b]

85. When you see…
Find the range
of f(x) on
You think…

86. Find the range of f(x) on

87. When you see…
You think…

88. Second Derivative Test

89. When you see…
You think…

90. Find inflection points

91. When you see…
You think…

92. .y = mx+b is tangent to f(x) at a point

93. When you see…
You think…

94. Horizontal tangent line

95. When you see…
You think…

96. Vertical tangent line to f(x)

97. Approximate the value f(0.1) of by using the
When you see…
Approximate the value f(0.1) of by using the
tangent line to f at x = 0
You think…

98. Approximate f(0.1) using tangent line to f(x) at x = 0

99. Find rates of change for volume problems
When you see…
Find rates of change for volume problems
You think…

100. Rates of Change of Volumes

101. Find rates of change for Pythagorean Theorem problems
When you see…
Find rates of change for Pythagorean Theorem problems
You think…

102. Pythagorean Rates of Change

103. When you see…
You think…

104. Average value of the function

105. When you see…
You think…

106. Average Rate of Change

107. Given v(t), find the total distance a particle travels on [a, b]
When you see…
Given v(t), find the total distance a particle travels on [a, b]
You think…

108. Given v(t), find the total distance a particle travels on [a,b]

109. Given v(t), find the change in position of a particle on [a, b]
When you see…
Given v(t), find the change in position of a particle on [a, b]
You think…

110. Given v(t), find the change in position of a particle on [a,b]

111. When you see…
You think…

112. Given v(t) and the initial position of a particle, find the position at t = a.

113. When you see…
You think…

114. Fundamental Theorem

115. When you see…
You think…

116. Fundamental Theorem, again Chain Rule, too

117. Find area using left Riemann sums
When you see…
Find area using left Riemann sums
You think…

118. Area using left Riemann sums

119. Find area using right Riemann sums
When you see…
Find area using right Riemann sums
You think…

120. Area using right Riemann sums

121. Find area using midpoint rectangles
When you see…
Find area using midpoint rectangles
You think…

122. Area using midpoint rectangles

123. Find area using trapezoids
When you see…
Find area using trapezoids
You think…

124. Area using trapezoids

125. When you see… You think…
Describe how you can tell if rectangle or trapezoid approximations over- or under-estimate area.
You think…

126. Over- or Under-estimates

127. When you see…
Given , find
You think…

128. Given area under a curve and vertical shift, find the new area under the curve

129. When you see…
Given , draw a
slope field
You think…

130. Draw a slope field of dy/dx

131. y is increasing proportionally to y
When you see…
y is increasing proportionally to y
You think…

132. .y is increasing proportionally to y

133. Solve the differential equation …
When you see…
Solve the differential equation …
You think…

134. Solve the differential equation...

135. When you see…
Given a base, cross sections perpendicular to the x-axis that are squares
You think…

136. Semi-circular cross sections perpendicular to the x-axis

137. anti-derivative of f is F, find F(b)
When you see…
Given the value of F(a) and the fact that the
anti-derivative of f is F, find F(b)
You think…

138. Given F(a) and the that the anti-derivative of f is F, find F(b)

139. When you see…
Meaning of
You think…

140. Meaning of the integral of f(t) from a to x

141. When you see…
Given v(t) and s(0), find the greatest distance from the origin of a particle on [a, b]
You think…

142. Given v(t) and s(0), find the greatest distance from the origin of a particle on [a, b]

143. When you see…

144. the amount of water in
the tank at m minutes
You think…

145. Amount of water in the tank at t minutes

146. b) the rate the water
amount is changing
at m
You think…

147. Rate the amount of water is changing at t = m

148. c) the time when the
water is at a minimum
You think…

149. The time when the water is at a minimum

150. When you see…
You think…

151. Area between f(x) and g(x) on [a,b]

152. When you see…
You think…

153. Volume generated by rotating area between f(x) and g(x) about the x-axis

154. When you see…
Given v(t) and s(0),
find s(t)
You think…

155. Given v(t) and s(0), find s(t)

156. When you see… You think…
Find the line x = c that divides the area under f(x) on [a, b] into two equal areas
You think…

157. Find the x=c so the area under f(x) is divided equallyOR

158. When you see…
You think…

159. Semi-circular cross sections perpendicular to the x-axis