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