When you see… Find the zeros You think…

To find the zeros...

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

Even function

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

Odd function

You think… When you see… Show that exists

Show exists Show that

You think… When you see…

Find Limit with calculator

You think… When you see…

Find limits, no calculator

You think… When you see…

Find limit with calculator

You think… When you see…

Find limit, no calculator

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)

Find the domain of f(x)

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

.f(x) is continuous

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

Slope of tangent line

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

Equation of the tangent line

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

Equation of the normal line

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

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

You think… When you see…

Intermediate Value Theorem (IVT)

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

f(x) 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) Find f ‘ ( a)

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…

You think… When you see…

Relative maximum

You think… When you see…

Concave Down

You think… When you see…

Points of Inflection

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

You think… When you see…

Derivative of Inverse Function

You think… When you see…

Derivative of the inverse of f(x)

You think… When you see…

Derivative Rules

You think… When you see…

Implicit Differentiation

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

Chain Rule

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

Minimum value of a function

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

Minimum slope of a function

You think… When you see… Find critical numbers

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…

Rolle’s Theorem

You think… When you see…

Mean Value Theorem

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

Find the range of f(x) on

You think… When you see…

Second Derivative Test

You think… When you see…

Find inflection points

You think… When you see…

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

You think… When you see…

Horizontal tangent line

You think… When you see…

Vertical tangent line to f(x)

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

Rates of Change of Volumes

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

Pythagorean Rates of Change

You think… When you see…

Average value of the function

You think… When you see…

Average Rate of Change

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]

You think… When you see…

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

You think… When you see…

Fundamental Theorem

You think… When you see…

Fundamental Theorem, again Chain Rule, too

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

Area using left Riemann sums

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

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

Area using trapezoids

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

Over- or Under-estimates

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

Draw a slope field of dy/dx

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]

When you see…

You think… the amount of water in the tank at m minutes

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

You think… When you see…

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

You think… When you see…

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

You think… When you see…

Semi-circular cross sections perpendicular to the x-axis