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position time position time tangent! Derivatives are the slope of a function at a point Slope of x...

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Calculus in 10 Minutes or Less
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Page 1: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

Calculus in 10 Minutes or Less

Page 2: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

Slope

position

time

Page 3: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

Slope

position

time

tangent!

Page 4: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

Derivatives

Derivatives are the slope of a function at a point Slope of x vs. t

velocity - describes how position changes over time Slope of v vs. t

acceleration - describes how velocity changes over time

Slope of a vs. t jerk - describes how acceleration changes over time

Page 5: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

Derivatives

Page 6: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

Derivative Rules

Page 7: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

If the position of an object is described by the function

What are the velocity and acceleration functions?

Page 8: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

Area

velocity

time

Easy!

Page 9: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

Area

velocity

time

Harder!!!

Page 10: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

Integrals

Integrals are anti-derivatives Graphically, integrals are the area

under a curve Area under a v vs. t graph = Displacement

Page 11: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

Integrals

Page 12: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

Integral Rules

Page 13: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

An object’s acceleration is described by a(t) = 2t. Find the velocity and position functions.

Page 14: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

Initial ConditionsIf x = 5 when t = 0, what is the displacement function for this velocity function?

-so- -so-

Page 15: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

Definite Integrals

Taking the integral from one point to another.

Same rules apply, but don’t have to do “+C”

Page 16: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

Find the displacement from t = 2 seconds to t = 4 seconds for the velocity function

Page 17: position time position time tangent! Derivatives are the slope of a function at a point Slope of x vs. t velocity - describes how position changes.

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