Velocity and Other Rates of Change

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3.4 Velocity and Other Rates of Change

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Presentation transcript:

Velocity and Other Rates of Change Chapter 3 Derivatives Section 3.4 Velocity and Other Rates of Change

Quick Review

Quick Review

Quick Review Solutions

Quick Review Solutions

What you’ll learn about Instantaneous rates of change Motion on a line Acceleration as the second derivative Modeling vertical motion and particle motion The derivative as a measure of sensitivity to change Marginal cost and marginal revenue … 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