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Unit 4: Contextual Applications of Differentiation

AP Calculus AB — Note Packet

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Key Terms

Derivative (f'(x) or dy/dx)

The derivative represents the ______ rate of change of a dependent variable with respect to an independent variable.

Units of the Derivative

The units of f'(x) are always the units of the ______ divided by the units of the _______________.

Velocity (v(t))

Velocity is the ______ of the position function, s'(t), and indicates both speed and _______________.

Acceleration (a(t))

Acceleration is the derivative of the ______ function, v'(t), and the _______________ derivative of the position function, s''(t).

Speed

Speed is the ______ _______________ of velocity, |v(t)|, and is always a _______________ value.

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