AP CALCULUS AB Chapter 3: Derivatives Section 3.4: Velocity and Other Rates of Change.

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AP CALCULUS AB Chapter 3: Derivatives Section 3.4: Velocity and Other Rates of Change

What you’ll learn about  Instantaneous Rates of change  Motion Along a Line  Sensitivity to Change  Derivatives in Economics … and why Derivatives give the rates at which things change in the world.

Instantaneous Rates of Change

Example Instantaneous Rates of Change

Ex: Find the rate of change of the Area of a square with respect to the length of a side when s = 4cm.

Motion Along a Line

Instantaneous Velocity

Speed

Acceleration

Free-fall Constants (Earth)

Section 3.4 – Velocity and Other Rates of Change  Position of an object (neglecting air resistance) under the influence of gravity, can be represented by where s 0 = original height of the object v 0 = original velocity of the object g = acceleration due to gravity

Example Finding Velocity

Sensitivity to Change When a small change in x produces a large change in the value of a function f(x), we say that the function is relatively sensitive to changes in x. The derivative f’(x) is a measure of this sensitivity. This has applications in Biology and Physics.

Derivatives in Economics

Example Derivatives in Economics

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