When you see

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
When you see
Find equation of the line normal to f(x) at (a,
b)
You think
6
Equation of the normal line
7
When you see
Show that f(x) is even
You think
8
Even function
9
When you see
Show that f(x) is odd
You think
10
Odd function
11
When you see
Find the interval where f(x) is increasing
You think
12
f(x) increasing
13
When you see
Find the interval where the slope of f (x) is
increasing
You think
14
Slope of f (x) is increasing
15
When you see
Find the minimum value of a function
You think
16
Minimum value of a function
17
When you see
Find the minimum slope of a function
You think
18
Minimum slope of a function
19
When you see
Find critical numbers
You think
20
Find critical numbers
21
When you see
Find inflection points
You think
22
Find inflection points
23
When you see
Show that exists
You think
24
Show exists

• Show that

25
When you see
Show that f(x) is continuous
You think
26
.f(x) is continuous
27
When you see
Find vertical asymptotes of f(x)
You think
28
Find vertical asymptotes of f(x)

• Factor/cancel f(x)
• then
• Set denominator 0

29
When you see
Find horizontal asymptotes of f(x)
You think
30
Find horizontal asymptotes of f(x)
31
When you see
Find the average rate of change of f(x) on a, b
You think
32
Average rate of change of f(x)

• Find
• f (b) - f ( a)
• b - a

33
When you see
Find the instantaneous rate of change of f(x)
at (a, b)
You think
34
Instantaneous rate of change of f(x)

• Find f ( a)

35
When you see
You think
36
Average value of the function
37
When you see
Find the absolute maximum of f(x) on a, b
You think
38
Find the absolute minimum of f(x)
39
When you see
Show that a piecewise function is differentiable
at the point a where the function rule splits
You think
40
Show a piecewise function is differentiable at
xa
41
When you see
Given s(t) (position function), find v(t)
You think
42
Given position s(t), find v(t)
43
When you see
Given v(t), find how far a particle travels on
a, b
You think
44
Given v(t), find how far a particle travels on
a,b
45
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
When you see
Given v(t), determine if a particle is speeding
up at t a
You think
48
Given v(t), determine if the particle is speeding
up at ta
49
When you see
Given v(t) and s(0), find s(t)
You think
50
Given v(t) and s(0), find s(t)
51
When you see
Show that Rolles Theorem holds on a, b
You think
52
Show that Rolles Theorem holds on a,b
53
When you see
Show that the Mean Value Theorem holds on a, b
You think
54
Show that the MVT holds on a,b
55
When you see
Find the domain of f(x)
You think
56
Find the domain of f(x)
57
When you see
Find the range of f(x) on a, b
You think
58
Find the range of f(x) on a,b
59
When you see
Find the range of f(x) on
You think
60
Find the range of f(x) on
61
When you see
Find f (x) by definition
You think
62
Find f ( x) by definition
63
When you see
Find the derivative of the inverse of f(x) at x
a
You think
64
Derivative of the inverse of f(x) at xa
Set a f(b) solve for b. Use b for
65
When you see
y is increasing proportionally to y
You think
66
.y is increasing proportionally to y
67
When you see
Find the line x c that divides the area under
f(x) on a, b into two equal areas
You think
68
Find the xc so the area under f(x) is divided
equally
69
When you see

You think
70
Fundamental Theorem
71
When you see

You think
72
Fundamental Theorem, again
73
When you see
The rate of change of population is
You think
74
Rate of change of a population
75
When you see
The line y mx b is tangent to f(x) at (a, b)
You think
76
.y mxb is tangent to f(x) at (a,b)
77
When you see
Find area using left Riemann sums
You think
78
Area using left Riemann sums
79
When you see
Find area using right Riemann sums
You think
80
Area using right Riemann sums
81
When you see
Find area using midpoint rectangles
You think
82
Area using midpoint rectangles
83
When you see
Find area using trapezoids
You think
84
Area using trapezoids
85
When you see
Solve the differential equation
You think
86
Solve the differential equation...
87
When you see
Meaning of
You think
88
Meaning of the integral of f(t) from a to x
89
When you see
Given a base, cross sections perpendicular to the
x-axis that are squares
You think
90
Square cross sections perpendicular to the x-axis
91
When you see
Find where the tangent line to f(x) is horizontal
You think
92
Horizontal tangent line
93
When you see
Find where the tangent line to f(x) is vertical
You think
94
Vertical tangent line to f(x)
95
When you see

Find the minimum acceleration given v(t)
You think
96
Given v(t), find minimum acceleration
97
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
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
100
Given F(a) and the that the anti-derivative of
f is F, find F(b)
101
When you see
Find the derivative of f(g(x))
You think
102
Find the derivative of f(g(x))
103
When you see
Given , find
You think
104
Given area under a curve and vertical shift, find
the new area under the curve
105
When you see
Given a graph of find where f(x) is
increasing
You think
106
Given a graph of f (x) , find where f(x) is
increasing
107
When you see

Given v(t) and s(0), find the greatest distance
from the origin of a particle on a, b
You think
108
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

• the amount of water in
• the tank at m minutes

You think
111
Amount of water in the tank at t minutes
112
b) the rate the water amount is changing
at m
You think
113
Rate the amount of water is changing at t m
114
c) the time when the water is at a
minimum

You think
115
The time when the water is at a minimum
116
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.
You think
117
(No Transcript)
118
When you see

Given , draw a slope field
You think
119
Draw a slope field of dy/dx
120
When you see
Find the area between curves f(x) and g(x) on
a,b
You think
121
Area between f(x) and g(x) on a,b
122
When you see
Find the volume if the area between the curves
f(x) and g(x) is rotated about the x-axis
You think
123
Volume generated by rotating area between f(x)
and g(x) about the x-axis