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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…

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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]**

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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]**

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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]**

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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]**

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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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