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1 When you see… Find the zeros You think…

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2 To find the zeros...

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

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4 Equation of the tangent line

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

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6 Equation of the normal line

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

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

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10 Slope of f (x) is increasing

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11 You think… When you see… Find critical numbers

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12 Find critical numbers

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13 You think… When you see… Find inflection points

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14 Find inflection points

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15 You think… When you see… Show that exists

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

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18. f(x) is continuous

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19 You think… When you see… Show that f(x) is differentiable at x = a

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20 f(x) is differentiable

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

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22 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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23 You think… When you see… Find horizontal asymptotes of f(x)

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24 Find horizontal asymptotes of f(x)

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

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26 Average rate of change of f(x) Find ARC(f) = f (b) - f ( a) b - a

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27 You think… When you see… Find the instantaneous rate of change of f(x) at x = a

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28 Instantaneous rate of change of f(x) Find f ‘ ( a)

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29 You think… When you see… Find the(absolute) max or minimum value of a function

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30 Local Minimum value of a function

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31 You think… When you see… Show that the only CP is a max/min

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32 Local Minimum value of a function

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

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

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35 You think… When you see… Total Distance

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

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

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

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39 You think… When you see… determine if a particle is speeding up

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40 Given v(t), determine if the particle is speeding up

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41 You think… When you see… Mean Value Theorem

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42 Show that the MVT holds on [a,b]

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43 You think… When you see… Relationship between f f’ and f’’

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44 f” + - f’ + - f

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

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46 Find f ‘( x) by definition

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47 You think… When you see… FTC part 2.

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48 FTC

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49 You think… When you see…

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50 FTC part 2

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51 You think… When you see…

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52 Fundamental Theorem, again

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

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54 Derivative of the inverse of f(x)

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55 You think… When you see… y is increasing proportionally to y

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

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58 Rate of change of a population

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59 You think… When you see… Find area using Riemann/Trapezoidal sums

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60 Area using Riemann sums

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61 You think… When you see… Solve the differential equation …

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62 Solve the differential equation...

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

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

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

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

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70 Find the derivative of f(g(x)) Think... Chain Rule

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71 You think… When you see… estimate where c is between a and b.

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72 MVT

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73 You think… When you see… Approximate f(c) using linearization

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75 You think… When you see… Volume of Revolution

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76 (1) dx or dy, (2) washer or disk, …

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77 You think… When you see… Find the area between curves f(x) and g(x)

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

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79 You think… When you see…

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80 Average value of the function

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81 You think… When you see…

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83 You think… When you see…

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85 You think… When you see…

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f ’(x) 86

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87 You think… When you see…

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U substitution 88

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