When you see… Find the zeros You think…
To find the zeros...
When you see… Show that f(x) is even You think…
Even function
When you see… Show that f(x) is odd You think…
Odd function
When you see… Show that exists You think…
Show exists Show that
When you see… You think…
Find Limit with calculator
When you see… You think…
Find limits, no calculator
When you see… You think…
Find limit with calculator
When you see… You think…
Find limit, no calculator
Find horizontal asymptotes of f(x) When you see… Find horizontal asymptotes of f(x) You think…
Find horizontal asymptotes of f(x)
When you see… Find vertical asymptotes of f(x) You think…
Find vertical asymptotes of f(x)
When you see… Find the domain of f(x) You think…
Find the domain of f(x)
Show that f(x) is continuous When you see… Show that f(x) is continuous You think…
.f(x) is continuous
Find the slope of the tangent line to f(x) at x = a When you see… Find the slope of the tangent line to f(x) at x = a You think…
Slope of tangent line
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 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 f (b) - f ( a) b - a
When you see… You think…
Intermediate Value Theorem (IVT)
Find the interval where f(x) is increasing When you see… Find the interval where f(x) is increasing You think…
f(x) increasing
Find the interval where the slope of f (x) is increasing When you see… Find the interval where the slope of f (x) is increasing You think…
Slope of f (x) is increasing
Find the instantaneous rate of change of f(x) When you see… Find the instantaneous rate of change of f(x) on [a, b] You think…
Instantaneous rate of change of f(x) Find f ‘ ( a)
Given s(t) (position function), find v(t) When you see… Given s(t) (position function), find v(t) You think…
Given position s(t), find v(t)
Find f ’(x) by the limit definition When you see… Find f ’(x) by the limit definition You think…
Find f ‘( x) by definition frequently asked backwards
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]
Given v(t), determine if a particle is speeding up at 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
Given a graph of find where f(x) is increasing When you see… You think…
Given a graph of f ‘(x) , find where f(x) is increasing
When you see… You think…
When you see… You think…
Relative maximum
When you see… You think…
Concave Down
When you see… You think…
Points of Inflection
When you see… Show that a piecewise function is differentiable at the point a where the function rule splits You think…
Show a piecewise function is differentiable at x=a
When you see… You think…
Derivative of Inverse Function
When you see… You think…
Derivative of the inverse of f(x)
When you see… You think…
Derivative Rules
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Implicit Differentiation
When you see… Find the derivative of f(g(x)) You think…
Chain Rule
Find the minimum value of a function When you see… Find the minimum value of a function You think…
Minimum value of a function
Find the minimum slope of a function When you see… Find the minimum slope of a function You think…
Minimum slope of a function
When you see… Find critical numbers You think…
Find critical numbers
Find the absolute maximum of f(x) When you see… Find the absolute maximum of f(x) You think…
Find the absolute minimum of f(x)
When you see… You think…
Rolle’s Theorem
When you see… You think…
Mean Value Theorem
When you see… Find the range of f(x) on [a, b] You think…
Find the range of f(x) on [a,b]
When you see… Find the range of f(x) on You think…
Find the range of f(x) on
When you see… You think…
Second Derivative Test
When you see… You think…
Find inflection points
When you see… You think…
.y = mx+b is tangent to f(x) at a point
When you see… You think…
Horizontal tangent line
When you see… You think…
Vertical tangent line to f(x)
Approximate the value f(0.1) of by using the When you see… Approximate the value f(0.1) of by using the tangent line to f at x = 0 You think…
Approximate f(0.1) using tangent line to f(x) at x = 0
Find rates of change for volume problems When you see… Find rates of change for volume problems You think…
Rates of Change of Volumes
Find rates of change for Pythagorean Theorem problems When you see… Find rates of change for Pythagorean Theorem problems You think…
Pythagorean Rates of Change
When you see… You think…
Average value of the function
When you see… You think…
Average Rate of Change
Given v(t), find the total distance a particle travels on [a, b] When you see… Given v(t), find the total distance a particle travels on [a, b] You think…
Given v(t), find the total distance a particle travels on [a,b]
Given v(t), find the change in position of a particle on [a, b] When you see… Given v(t), find the change in position of a particle on [a, b] You think…
Given v(t), find the change in position of a particle on [a,b]
When you see… You think…
Given v(t) and the initial position of a particle, find the position at t = a.
When you see… You think…
Fundamental Theorem
When you see… You think…
Fundamental Theorem, again Chain Rule, too
Find area using left Riemann sums When you see… Find area using left Riemann sums You think…
Area using left Riemann sums
Find area using right Riemann sums When you see… Find area using right Riemann sums You think…
Area using right Riemann sums
Find area using midpoint rectangles When you see… Find area using midpoint rectangles You think…
Area using midpoint rectangles
Find area using trapezoids When you see… Find area using trapezoids You think…
Area using trapezoids
When you see… You think… Describe how you can tell if rectangle or trapezoid approximations over- or under-estimate area. You think…
Over- or Under-estimates
When you see… Given , find You think…
Given area under a curve and vertical shift, find the new area under the curve
When you see… Given , draw a slope field You think…
Draw a slope field of dy/dx
y is increasing proportionally to y When you see… y is increasing proportionally to y You think…
.y is increasing proportionally to y
Solve the differential equation … When you see… Solve the differential equation … You think…
Solve the differential equation...
When you see… Given a base, cross sections perpendicular to the x-axis that are squares You think…
Semi-circular cross sections perpendicular to the x-axis
anti-derivative of f is F, find F(b) When you see… Given the value of F(a) and the fact that the anti-derivative of f is F, find F(b) You think…
Given F(a) and the that the anti-derivative of f is F, find F(b)
When you see… Meaning of You think…
Meaning of the integral of f(t) from a to x
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]
When you see…
the amount of water in the tank at m minutes You think…
Amount of water in the tank at t minutes
b) the rate the water amount is changing at m You think…
Rate the amount of water is changing at t = m
c) the time when the water is at a minimum You think…
The time when the water is at a minimum
When you see… You think…
Area between f(x) and g(x) on [a,b]
When you see… You think…
Volume generated by rotating area between f(x) and g(x) about the x-axis
When you see… Given v(t) and s(0), find s(t) You think…
Given v(t) and s(0), find s(t)
When you see… You think… 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 OR
When you see… You think…
Semi-circular cross sections perpendicular to the x-axis