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# When you see… - PowerPoint PPT Presentation

When you see…. You think…. Find the zeros. To find the zeros. When you see…. Find equation of the line tangent to f ( x ) at ( a , b ). You think…. Equation of the tangent line. When you see…. Find equation of the line normal to f ( x ) at ( a , b ). You think….

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## PowerPoint Slideshow about 'When you see…' - eddy

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Presentation Transcript

### When you see…

You think…

Find the zeros

Find equation of the line tangent to f(x) at(a, b)

You think…

Find equation of the line normal to f(x) at(a, b)

You think…

Show that f(x) is even

You think…

Show that f(x) is odd

You think…

Find the interval where f(x) is increasing

You think…

f(x) increasing

Find the interval where the slope of f (x) is increasing

You think…

Slope of f (x) is increasing

Find the minimum value of a function

You think…

Find the minimum slope of a function

You think…

Find critical numbers

You think…

Find inflection points

You think…

Show that exists

You think…

Show that

Show that f(x) is continuous

You think…

.f(x) is continuous

Find vertical

asymptotes of f(x)

You think…

Factor/cancel f(x)

Set denominator = 0

Find horizontal asymptotes of f(x)

You think…

Find the average rate of change of f(x) at[a, b]

You think…

Find

f (b) - f ( a)

b - a

Find the instantaneous rate of change of f(x)

on[a, b]

You think…

Find f ‘ ( a)

You think…

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

You think…

Show that a piecewise function is differentiable at the point awhere the function rule splits

You think…

Given s(t) (position function), findv(t)

You think…

Given v(t), find how far a particle travels on[a, b]

You think…

Find the average velocity of a particle

on[a, b]

You think…

Given v(t), determine if a particle is speeding up at

t = k

You think…

Given v(t) and s(0),

find s(t)

You think…

Show that Rolle’s Theorem holds on[a, b]

You think…

Show that the Mean Value Theorem holds

on[a, b]

You think…

Find the domain

of f(x)

You think…

Find the range

of f(x) on [a, b]

You think…

Find the range

of f(x) on

You think…

Find f ’(x) by definition

You think…

Find f ‘( x) by definition

Find the derivative of the inverse of f(x) at x = a

You think…

Value ofy is increasing proportionally to y

You think…

Value of.y is increasing proportionally to y

Find the line x = c that divides the area under f(x) on [a, b] into two equal areas

You think…

You think…

You think…

The rate of change of population is …

You think…

Rate of change of a population

The line y = mx + b is tangent to f(x) at (a, b)

You think…

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

Find area using left Riemann sums

You think…

Find area using right Riemann sums

You think…

Find area using midpoint rectangles

You think…

Find area using trapezoids

You think…

Solve the differential equation …

You think…

Meaning of

You think…

Given a base, cross sections perpendicular to the x-axis that are squares

You think…

Find where the tangent line to f(x) is horizontal

You think…

Find where the tangent line to f(x) is vertical

You think…

Find the minimum acceleration given v(t)

You think…

Approximate the value f(0.1) of by using the

tangent line to f atx = 0

You think…

Given the value of F(a) and the fact that the

anti-derivative of f is F, findF(b)

You think…

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

Find the derivative of

f(g(x))

You think…

Given , find

You think…

When you see… area under the curve

Given a graph of

find where f(x) is

increasing

You think…

When you see… area under the curve

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

You think…

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

When you see… area under the curve

Given a water tank with g gallons initially being filled at the rate of F(t) gallons/min and emptied at the rate of E(t) gallons/min on

, find

You think…

b) the rate the water area under the curve

amount is changing

at m

You think…

c) the time when the area under the curve

water is at a minimum

You think…

When you see… area under the curve

Given a chart of x and f(x) on selected values between a and b, estimate where c is between aandb.

You think…

When you see… area under the curve

Given , draw a

slope field

You think…

Draw a slope field of dy/dx area under the curve

When you see… area under the curve

Find the area between curves f(x) and g(x) on[a,b]

You think…

When you see… area under the curve

Find the volume if the area between thecurves f(x) and g(x) is