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.

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Presentation transcript:

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

Motion Along a Line

Instantaneous Velocity

Speed

Acceleration

Free-fall Constants (Earth)

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.

Derivatives in Economics

Example Derivatives in Economics