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

2. To find the zeros...

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

4. Equation of the tangent line

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

6. Equation of the normal line

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

8. Even function

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

10. Odd function

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

12. f(x) increasing

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

14. Slope of f (x) is increasing

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

16. Relative Minimum value of a function Relative Minimum value of a function

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

18. Relative Minimum slope of a function

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

21. You think… When you see… Find inflection points

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

24. Show exists Show that

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

26. . f(x) is continuous

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

28. Find vertical asymptotes of f(x) Factor/cancel f(x) Set denominator = 0

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

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

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

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

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

35. You think… When you see…

36. Average value of the function

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

38. Find the absolute minimum of f(x)

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

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

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

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

43. You think… When you see… Given v(t), find how far a particle travels on [a, b]

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

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

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

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

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

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

51. You think… When you see… Show that Rolle’s Theorem holds on [a, b]

53. You think… When you see… Show that the Mean Value Theorem holds on [a, b]

54. Show that the MVT holds on [a,b]

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

56. Find the domain of f(x)

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

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

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

60. Find the range of f(x) on

61. You think… When you see… Find f ’ (x) by definition

62. Find f ‘( x) by definition

63. You think… When you see… Find the derivative of the inverse of f(x) at x = a

64. Derivative of the inverse of f(x) at x=a

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

66. y is increasing proportionally to y. y is increasing proportionally to y

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

68. Find the x=c so the area under f(x) is divided equally

69. You think… When you see…

70. Fundamental Theorem

71. You think… When you see…

72. Fundamental Theorem, again

73. You think… When you see… The rate of change of population is …

74. Rate of change of a population

75. You think… When you see… The line y = mx + b is tangent to f(x) at (a, b)

76. y = mx+b is tangent to f(x) at (a,b). y = mx+b is tangent to f(x) at (a,b)

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

78. Area using left Riemann sums

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

80. Area using right Riemann sums

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

82. Area using midpoint rectangles

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

84. Area using trapezoids

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

86. Solve the differential equation...

87. You think… When you see… Meaning of

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

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

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

91. You think… When you see… Find where the tangent line to f(x) is horizontal

92. Horizontal tangent line

93. You think… When you see… Find where the tangent line to f(x) is vertical

94. Vertical tangent line to f(x)

95. You think… When you see… Find the minimum acceleration given v(t)

96. Given v(t), find minimum acceleration

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

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

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

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

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

102. Find the derivative of f(g(x))

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

104. Given area under a curve and vertical shift, find the new area under the curve You can also consider this from a conceptual viewpoint: You are adding a rectangle under the area of f(x): the area of the rectangle is (b-a)k

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

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

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

109. When you see… Given a water tank with g gallons initially being filled at the rate of F(t) gallons/min and emptied at the rate of E(t) gallons/min on, find

110. You think… a)the amount of water in the tank at m minutes

111. Amount of water in the tank at t minutes

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

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

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

115. The time when the water is at a minimum

116. You think… When you see… Given a chart of x and f(x) on selected values between a and b, estimate where c is between a and b.

117. estimate where c is between a and b.

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

119. Draw a slope field of dy/dx

120. You think… When you see… Find the area between curves f(x) and g(x) on [a,b]

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

122. You think… When you see… Find the volume if the area between the curves f(x) and g(x) is rotated about the x -axis

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

124. You think… When you see… Find if

126. You think… When you see… Find

128. You think… When you see…

130. You think… When you see… Find

132. You think… When you see… The position vector of a particle moving the plane is

133. You think… When you see… a) Find the velocity

135. You think… When you see… b) Find the acceleration

137. You think… When you see… c) Find the speed

139. You think… When you see… a) Given the velocity vector And position at time 0, find the position vector

140. Given the velocity vector And position at time 0, find the position vector

141. You think… When you see… b) When does the particle stop?

143. You think… When you see… c) Find the slope of the tangent line to the vector at t 1