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When you see… - PowerPoint PPT Presentation


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When you see…. You think…. Find the zeros. To find the zeros. When you see…. Find equation of the line tangent to f ( x ) at ( a , b ). You think…. Equation of the tangent line. When you see…. Find equation of the line normal to f ( x ) at ( a , b ). You think….

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Presentation Transcript
when you see

When you see…

You think…

Find the zeros

slide3

When you see…

Find equation of the line tangent to f(x) at(a, b)

You think…

slide5

When you see…

Find equation of the line normal to f(x) at(a, b)

You think…

slide7

When you see…

Show that f(x) is even

You think…

slide9

When you see…

Show that f(x) is odd

You think…

slide11

When you see…

Find the interval where f(x) is increasing

You think…

slide13

When you see…

Find the interval where the slope of f (x) is increasing

You think…

slide15

When you see…

Find the minimum value of a function

You think…

slide17

When you see…

Find the minimum slope of a function

You think…

slide19

When you see…

Find critical numbers

You think…

slide21

When you see…

Find inflection points

You think…

slide23

When you see…

Show that exists

You think…

show exists
Show exists

Show that

slide25

When you see…

Show that f(x) is continuous

You think…

slide27

When you see…

Find vertical

asymptotes of f(x)

You think…

find vertical asymptotes of f x
Find vertical asymptotes of f(x)

Factor/cancel f(x)

Set denominator = 0

slide29

When you see…

Find horizontal asymptotes of f(x)

You think…

slide31

When you see…

Find the average rate of change of f(x) at[a, b]

You think…

average rate of change of f x
Average rate of change of f(x)

Find

f (b) - f ( a)

b - a

slide33

When you see…

Find the instantaneous rate of change of f(x)

on[a, b]

You think…

slide35

When you see…

You think…

slide37

When you see…

Find the absolute minimum of f(x) on[a, b]

You think…

slide39

When you see…

Show that a piecewise function is differentiable at the point awhere the function rule splits

You think…

slide41

When you see…

Given s(t) (position function), findv(t)

You think…

slide43

When you see…

Given v(t), find how far a particle travels on[a, b]

You think…

slide45

When you see…

Find the average velocity of a particle

on[a, b]

You think…

slide47

When you see…

Given v(t), determine if a particle is speeding up at

t = k

You think…

slide49

When you see…

Given v(t) and s(0),

find s(t)

You think…

slide51

When you see…

Show that Rolle’s Theorem holds on[a, b]

You think…

slide53

When you see…

Show that the Mean Value Theorem holds

on[a, b]

You think…

slide55

When you see…

Find the domain

of f(x)

You think…

slide57

When you see…

Find the range

of f(x) on [a, b]

You think…

slide59

When you see…

Find the range

of f(x) on

You think…

slide61

When you see…

Find f ’(x) by definition

You think…

slide63

When you see…

Find the derivative of the inverse of f(x) at x = a

You think…

slide65

When you see…

Value ofy is increasing proportionally to y

You think…

slide67

When you see…

Find the line x = c that divides the area under f(x) on [a, b] into two equal areas

You think…

slide69

When you see…

You think…

slide71

When you see…

You think…

slide73

When you see…

The rate of change of population is …

You think…

slide75

When you see…

The line y = mx + b is tangent to f(x) at (a, b)

You think…

slide77

When you see…

Find area using left Riemann sums

You think…

slide79

When you see…

Find area using right Riemann sums

You think…

slide81

When you see…

Find area using midpoint rectangles

You think…

slide83

When you see…

Find area using trapezoids

You think…

slide85

When you see…

Solve the differential equation …

You think…

slide87

When you see…

Meaning of

You think…

slide89

When you see…

Given a base, cross sections perpendicular to the x-axis that are squares

You think…

slide91

When you see…

Find where the tangent line to f(x) is horizontal

You think…

slide93

When you see…

Find where the tangent line to f(x) is vertical

You think…

slide95

When you see…

Find the minimum acceleration given v(t)

You think…

slide97

When you see…

Approximate the value f(0.1) of by using the

tangent line to f atx = 0

You think…

slide99

When you see…

Given the value of F(a) and the fact that the

anti-derivative of f is F, findF(b)

You think…

slide101

When you see…

Find the derivative of

f(g(x))

You think…

slide103

When you see…

Given , find

You think…

slide105

When you see…

Given a graph of

find where f(x) is

increasing

You think…

slide107

When you see…

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

You think…

slide109

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

slide110

the amount of water in

  • the tank at m minutes

You think…

slide112

b) the rate the water

amount is changing

at m

You think…

slide114

c) the time when the

water is at a minimum

You think…

slide116

When you see…

Given a chart of x and f(x) on selected values between a and b, estimate where c is between aandb.

You think…

slide118

When you see…

Given , draw a

slope field

You think…

slide120

When you see…

Find the area between curves f(x) and g(x) on[a,b]

You think…

slide122

When you see…

Find the volume if the area between thecurves f(x) and g(x) is

rotated about the x-axis

You think…