AB Calculus Question Strategies

When you see… Find the zeros You think…

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

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

You think… When you see… Show that exists

Show exists ,[object Object]

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

Find horizontal asymptotes of f(x)

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

Find vertical asymptotes of f(x)

You think… When you see… Find the domain of f ( x )

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

You think… When you see… Find the slope of the tangent line to f(x) at x = a

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

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

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

Average rate of change of f(x) ,[object Object],[object Object],[object Object]

Intermediate Value Theorem (IVT)

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

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

Slope of f (x) is increasing

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

Instantaneous rate of change of f(x) ,[object Object]

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

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

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

Find f ‘ ( x) by definition frequently asked backwards

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

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

You think… When you see… Given v ( t ) , determine if a particle is speeding up at t = k

Given v(t), determine if the particle is speeding up at t = k

You think… When you see… Given a graph of find where f ( x ) is increasing

Given a graph of f ‘(x) , find where f(x) is increasing

You think… When you see… Show that a piecewise function is differentiable at the point a where the function rule splits

Show a piecewise function is differentiable at x=a

Derivative of Inverse Function

Derivative of the inverse of f(x)

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

You think… When you see… Find the minimum value of a function

You think… When you see… Find the minimum slope of a function

You think… When you see… Find critical numbers

You think… When you see… Find the absolute maximum of f ( x )

Find the absolute minimum of f(x)

You think… When you see… Find the range of f ( x ) on [ a , b ]

Find the range of f(x) on [a,b]

You think… When you see… Find the range of f ( x ) on

. y = mx+b is tangent to f(x) at a point

You think… When you see… Approximate the value f (0.1) of by using the tangent line to f at x = 0

Approximate f(0.1) using tangent line to f(x) at x = 0

You think… When you see… Find rates of change for volume problems

You think… When you see… Find rates of change for Pythagorean Theorem problems

You think… When you see… Given v ( t ) , find the total distance a particle travels on [ a , b ]

Given v(t), find the total distance a particle travels on [a,b]

You think… When you see… Given v ( t ) , find the change in position of a particle on [ a , b ]

Given v(t), find the change in position of a particle on [a,b]

Given v(t) and the initial position of a particle, find the position at t = a .

Fundamental Theorem, again Chain Rule, too

You think… When you see… Find area using left Riemann sums

You think… When you see… Find area using right Riemann sums

You think… When you see… Find area using midpoint rectangles

Area using midpoint rectangles

You think… When you see… Find area using trapezoids

You think… When you see… Describe how you can tell if rectangle or trapezoid approximations over- or under-estimate area.

You think… When you see… Given , find

Given area under a curve and vertical shift, find the new area under the curve

You think… When you see… Given , draw a slope field

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

. y is increasing proportionally to y

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

Solve the differential equation...

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

Semi-circular cross sections perpendicular to the x-axis

You think… When you see… Given the value of F ( a ) and the fact that the anti-derivative of f is F , find F ( b )

Given F ( a ) and the that the anti-derivative of f is F , find F ( b )

You think… When you see… Meaning of

Meaning of the integral of f(t) from a to x

You think… When you see… Given v ( t ) and s (0) , find the greatest distance from the origin of a particle on [ a , b ]

Given v ( t ) and s (0) , find the greatest distance from the origin of a particle on [ a , b ]

You think… ,[object Object],[object Object]

Amount of water in the tank at t minutes

You think… b) the rate the water amount is changing at m

Rate the amount of water is changing at t = m

You think… c) the time when the water is at a minimum

The time when the water is at a minimum

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

Volume generated by rotating area between f(x) and g(x) about the x-axis

You think… When you see… Given v ( t ) and s (0), find s ( t )

Given v(t) and s(0), find s(t)

You think… When you see… Find the line x = c that divides the area under f ( x ) on [ a , b ] into two equal areas

Find the x=c so the area under f(x) is divided equally OR

AB Calculus Question Strategies

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AB Calculus Question Strategies