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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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f(x) increasing

Slope of f (x) is increasing

Show exists

Show that

.f(x) is continuous

Instantaneous rate of change of f(x)

Find f ‘ ( a)

You think…

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

You think…

Find f ‘( x) by definition

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…

Rate of change of a population

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

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

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)

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

Given a graph of f ‘(x) , find where f(x) is increasing area under the curve

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

- the amount of water in area under the curve
- the tank at m minutes

You think…

Amount of water in the tank at t minutes area under the curve

Rate the amount of water is changing at t = m area under the curve

The time when the water is at a minimum area under the curve

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…

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

Area between f(x) and g(x) on [a,b] area under the curve

When you see… area under the curve

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

rotated about the x-axis

You think…

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

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