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When you see… Find the zeros You think…
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To find the zeros...
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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…
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Equation of the tangent line
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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…
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Equation of the normal line
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Find the interval where f(x) is increasing
When you see… Find the interval where f(x) is increasing You think…
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Find the interval where
When you see… Find the interval where f’ (x) is increasing You think…
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Slope of f (x) is increasing
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When you see… Find critical numbers You think…
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Find critical numbers
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Find inflection points
When you see… Find inflection points You think…
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Find inflection points
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When you see… Show that exists You think…
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Show that f(x) is continuous
When you see… Show that f(x) is continuous You think…
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.f(x) is continuous
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Show that f(x) is differentiable at x = a
When you see… Show that f(x) is differentiable at x = a You think…
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f(x) is differentiable
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When you see… Find vertical asymptotes of f(x) You think…
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Find vertical asymptotes of f(x)
VA: Set denominator = 0 Note: it’s a hole (not a VA) if top = 0
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Find horizontal asymptotes of f(x)
When you see… Find horizontal asymptotes of f(x) You think…
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Find horizontal asymptotes of f(x)
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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…
![Find the average rate of change of f(x) at [a, b]](http://slideplayer.com/slide/2484178/9/images/25/Find+the+average+rate+of+change+of+f%28x%29+at+%5Ba%2C+b%5D.jpg "When you see… Find the average rate of change of f(x) at [a, b] You think…")
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Average rate of change of f(x)
Find ARC(f) = f (b) - f ( a) b - a
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Find the instantaneous rate of change of f(x)
When you see… Find the instantaneous rate of change of f(x) at x = a You think…
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Instantaneous rate of change of f(x)
Find f ‘ ( a)
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Find the(absolute) max or minimum value of a function
When you see… Find the(absolute) max or minimum value of a function You think…
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Local Minimum value of a function
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Show that the only CP is a max/min
When you see… Show that the only CP is a max/min You think…
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Local Minimum value of a function
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Given s(t) (position function),
When you see… Given s(t) (position function), find v(t) You think…
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Given position s(t), find v(t)
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When you see… Total Distance You think…
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Given v(t), find how far a particle travels on [a,b]
![Given v(t), find how far a particle travels on [a,b]](http://slideplayer.com/slide/2484178/9/images/36/Given+v%28t%29%2C+find+how+far+a+particle+travels+on+%5Ba%2Cb%5D.jpg "Given v(t), find how far a particle travels on [a,b]")
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Find the average velocity of a particle
When you see… Find the average velocity of a particle on [a, b] You think…
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Find the average rate of change on [a,b]
![Find the average rate of change on [a,b]](http://slideplayer.com/slide/2484178/9/images/38/Find+the+average+rate+of+change+on+%5Ba%2Cb%5D.jpg "Find the average rate of change on [a,b]")
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determine if a particle is speeding up
When you see… determine if a particle is speeding up You think…
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Given v(t), determine if the particle is speeding up
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When you see… Mean Value Theorem You think…
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Show that the MVT holds on [a,b]
![Show that the MVT holds on [a,b]](http://slideplayer.com/slide/2484178/9/images/42/Show+that+the+MVT+holds+on+%5Ba%2Cb%5D.jpg "Show that the MVT holds on [a,b]")
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Relationship between f f’ and f’’
When you see… Relationship between f f’ and f’’ You think…
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f” + - f’ f
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Find f ’(x) by definition
When you see… Find f ’(x) by definition You think…
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Find f ‘( x) by definition
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When you see… FTC part 2 . You think…
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FTC
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When you see… You think…
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FTC part 2
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When you see… You think…
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Fundamental Theorem, again
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Find the derivative of the inverse of f(x) at x = a
When you see… Find the derivative of the inverse of f(x) at x = a You think…
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Derivative of the inverse of f(x)
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y is increasing proportionally to y
When you see… y is increasing proportionally to y You think…
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The rate of change of population is …
When you see… The rate of change of population is … You think…
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Rate of change of a population
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Find area using Riemann/Trapezoidal sums
When you see… Find area using Riemann/Trapezoidal sums You think…
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Area using Riemann sums
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Solve the differential equation …
When you see… Solve the differential equation … You think…
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Solve the differential equation...
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Given a base, cross sections perpendicular to the x-axis that are
When you see… Given a base, cross sections perpendicular to the x-axis that are You think…
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Find where the tangent line to f(x) is horizontal
When you see… Find where the tangent line to f(x) is horizontal You think…
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Find where the tangent line to f(x) is vertical
When you see… Find where the tangent line to f(x) is vertical You think…
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When you see… Find the derivative of f(g(x)) You think…
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Find the derivative of f(g(x))
Think Chain Rule
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estimate where c is between a and b.
When you see… estimate where c is between a and b. You think…
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MVT
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Approximate f(c) using linearization
When you see… Approximate f(c) using linearization You think…
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When you see… Volume of Revolution You think…
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(1) dx or dy, (2) washer or disk, …
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Find the area between curves f(x) and g(x)
When you see… Find the area between curves f(x) and g(x) You think…
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Area between f(x) and g(x) on [a,b]
![Area between f(x) and g(x) on [a,b]](http://slideplayer.com/slide/2484178/9/images/78/Area+between+f%28x%29+and+g%28x%29+on+%5Ba%2Cb%5D.jpg "Area between f(x) and g(x) on [a,b]")
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When you see… You think…
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Average value of the function
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When you see… You think…
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When you see… You think…
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When you see… You think…
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f ’(x)
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When you see… You think…
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U substitution
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