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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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When you see l.jpg

When you see…

You think…

Find the zeros


To find the zeros l.jpg

To find the zeros...


Slide3 l.jpg

When you see…

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

You think…


Equation of the tangent line l.jpg

Equation of the tangent line


Slide5 l.jpg

When you see…

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

You think…


Equation of the normal line l.jpg

Equation of the normal line


Slide7 l.jpg

When you see…

Show that f(x) is even

You think…


Even function l.jpg

Even function


Slide9 l.jpg

When you see…

Show that f(x) is odd

You think…


Odd function l.jpg

Odd function


Slide11 l.jpg

When you see…

Find the interval where f(x) is increasing

You think…


F x increasing l.jpg

f(x) increasing


Slide13 l.jpg

When you see…

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

You think…


Slope of f x is increasing l.jpg

Slope of f (x) is increasing


Slide15 l.jpg

When you see…

Find the minimum value of a function

You think…


Minimum value of a function l.jpg

Minimum value of a function


Slide17 l.jpg

When you see…

Find the minimum slope of a function

You think…


Minimum slope of a function l.jpg

Minimum slope of a function


Slide19 l.jpg

When you see…

Find critical numbers

You think…


Find critical numbers l.jpg

Find critical numbers


Slide21 l.jpg

When you see…

Find inflection points

You think…


Find inflection points l.jpg

Find inflection points


Slide23 l.jpg

When you see…

Show that exists

You think…


Show exists l.jpg

Show exists

Show that


Slide25 l.jpg

When you see…

Show that f(x) is continuous

You think…


F x is continuous l.jpg

.f(x) is continuous


Slide27 l.jpg

When you see…

Find vertical

asymptotes of f(x)

You think…


Find vertical asymptotes of f x l.jpg

Find vertical asymptotes of f(x)

Factor/cancel f(x)

Set denominator = 0


Slide29 l.jpg

When you see…

Find horizontal asymptotes of f(x)

You think…


Find horizontal asymptotes of f x l.jpg

Find horizontal asymptotes of f(x)


Slide31 l.jpg

When you see…

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

You think…


Average rate of change of f x l.jpg

Average rate of change of f(x)

Find

f (b) - f ( a)

b - a


Slide33 l.jpg

When you see…

Find the instantaneous rate of change of f(x)

on[a, b]

You think…


Instantaneous rate of change of f x l.jpg

Instantaneous rate of change of f(x)

Find f ‘ ( a)


Slide35 l.jpg

When you see…

You think…


Average value of the function l.jpg

Average value of the function


Slide37 l.jpg

When you see…

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

You think…


Find the absolute minimum of f x l.jpg

Find the absolute minimum of f(x)


Slide39 l.jpg

When you see…

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

You think…


Show a piecewise function is differentiable at x a l.jpg

Show a piecewise function is differentiable at x=a


Slide41 l.jpg

When you see…

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

You think…


Given position s t find v t l.jpg

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


Slide43 l.jpg

When you see…

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

You think…


Given v t find how far a particle travels on a b l.jpg

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


Slide45 l.jpg

When you see…

Find the average velocity of a particle

on[a, b]

You think…


Find the average rate of change on a b l.jpg

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


Slide47 l.jpg

When you see…

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

t = k

You think…


Given v t determine if the particle is speeding up at t k l.jpg

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


Slide49 l.jpg

When you see…

Given v(t) and s(0),

find s(t)

You think…


Given v t and s 0 find s t l.jpg

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


Slide51 l.jpg

When you see…

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

You think…


Show that rolle s theorem holds on a b l.jpg

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


Slide53 l.jpg

When you see…

Show that the Mean Value Theorem holds

on[a, b]

You think…


Show that the mvt holds on a b l.jpg

Show that the MVT holds on [a,b]


Slide55 l.jpg

When you see…

Find the domain

of f(x)

You think…


Find the domain of f x l.jpg

Find the domain of f(x)


Slide57 l.jpg

When you see…

Find the range

of f(x) on [a, b]

You think…


Find the range of f x on a b l.jpg

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


Slide59 l.jpg

When you see…

Find the range

of f(x) on

You think…


Find the range of f x on l.jpg

Find the range of f(x) on


Slide61 l.jpg

When you see…

Find f ’(x) by definition

You think…


Find f x by definition l.jpg

Find f ‘( x) by definition


Slide63 l.jpg

When you see…

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

You think…


Derivative of the inverse of f x at x a l.jpg

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


Slide65 l.jpg

When you see…

Value ofy is increasing proportionally to y

You think…


Value of y is increasing proportionally to y l.jpg

Value of.y is increasing proportionally to y


Slide67 l.jpg

When you see…

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

You think…


Find the x c so the area under f x is divided equally l.jpg

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


Slide69 l.jpg

When you see…

You think…


Fundamental theorem l.jpg

Fundamental Theorem


Slide71 l.jpg

When you see…

You think…


Fundamental theorem again l.jpg

Fundamental Theorem, again


Slide73 l.jpg

When you see…

The rate of change of population is …

You think…


Rate of change of a population l.jpg

Rate of change of a population


Slide75 l.jpg

When you see…

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

You think…


Y mx b is tangent to f x at a b l.jpg

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


Slide77 l.jpg

When you see…

Find area using left Riemann sums

You think…


Area using left riemann sums l.jpg

Area using left Riemann sums


Slide79 l.jpg

When you see…

Find area using right Riemann sums

You think…


Area using right riemann sums l.jpg

Area using right Riemann sums


Slide81 l.jpg

When you see…

Find area using midpoint rectangles

You think…


Area using midpoint rectangles l.jpg

Area using midpoint rectangles


Slide83 l.jpg

When you see…

Find area using trapezoids

You think…


Area using trapezoids l.jpg

Area using trapezoids


Slide85 l.jpg

When you see…

Solve the differential equation …

You think…


Solve the differential equation l.jpg

Solve the differential equation...


Slide87 l.jpg

When you see…

Meaning of

You think…


Meaning of the integral of f t from a to x l.jpg

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


Slide89 l.jpg

When you see…

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

You think…


Square cross sections perpendicular to the x axis l.jpg

Square cross sections perpendicular to the x-axis


Slide91 l.jpg

When you see…

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

You think…


Horizontal tangent line l.jpg

Horizontal tangent line


Slide93 l.jpg

When you see…

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

You think…


Vertical tangent line to f x l.jpg

Vertical tangent line to f(x)


Slide95 l.jpg

When you see…

Find the minimum acceleration given v(t)

You think…


Given v t find minimum acceleration l.jpg

Given v(t), find minimum acceleration


Slide97 l.jpg

When you see…

Approximate the value f(0.1) of by using the

tangent line to f atx = 0

You think…


Approximate f 0 1 using tangent line to f x at x 0 l.jpg

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


Slide99 l.jpg

When you see…

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

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

You think…


Given f a and the that the anti derivative of f is f find f b l.jpg

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


Slide101 l.jpg

When you see…

Find the derivative of

f(g(x))

You think…


Find the derivative of f g x l.jpg

Find the derivative of f(g(x))


Slide103 l.jpg

When you see…

Given , find

You think…


Given area under a curve and vertical shift find the new area under the curve l.jpg

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


Slide105 l.jpg

When you see…

Given a graph of

find where f(x) is

increasing

You think…


Given a graph of f x find where f x is increasing l.jpg

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


Slide107 l.jpg

When you see…

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

You think…


Given v t and s 0 find the greatest distance from the origin of a particle on a b l.jpg

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


Slide109 l.jpg

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 l.jpg

  • the amount of water in

  • the tank at m minutes

You think…


Amount of water in the tank at t minutes l.jpg

Amount of water in the tank at t minutes


Slide112 l.jpg

b) the rate the water

amount is changing

at m

You think…


Rate the amount of water is changing at t m l.jpg

Rate the amount of water is changing at t = m


Slide114 l.jpg

c) the time when the

water is at a minimum

You think…


The time when the water is at a minimum l.jpg

The time when the water is at a minimum


Slide116 l.jpg

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 l.jpg

When you see…

Given , draw a

slope field

You think…


Draw a slope field of dy dx l.jpg

Draw a slope field of dy/dx


Slide120 l.jpg

When you see…

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

You think…


Area between f x and g x on a b l.jpg

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


Slide122 l.jpg

When you see…

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

rotated about the x-axis

You think…


Volume generated by rotating area between f x and g x about the x axis l.jpg

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


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