1 / 7

Concavity and Rates of Change

Concavity and Rates of Change. Lesson 2.5 . Changing Rate of Change. Note that the rate of change of the curve of the top of the gate is changing. Consider how it is changing … Increasing? Decreasing? What effect does that have on the curve?. Concavity and Rates of Change.

brooke
Download Presentation

Concavity and Rates of Change

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Concavity and Rates of Change Lesson 2.5

  2. Changing Rate of Change • Note that the rate of change of the curve of the top of the gate is changing Consider how it is changing … Increasing? Decreasing? What effect does that have on the curve?

  3. Concavity and Rates of Change • What do the graphs below have in common? • How are they different? Specifically, look at the changing rate of change Both are increasing functions The slope (rate of change) is increasing The slope (rate of change) is decreasing

  4. Concavity and Rates of Change Slope is becoming more positive • An increasing positiverate of change is concave UP • A decreasing positiverate of change isconcave DOWN Slope is becoming less positive

  5. Concavity and Rates of Change • Increasing negativerate of change is concave DOWN • Decreasing negativerate of change isconcave UP Slope is becoming more negative Slope is becoming less negative

  6. Try It Out • Given the following table • Calculate the rates of change for successive pairs of points – are the slopes increasing or decreasing? • Predict concave up or down • Now Plot the points • Concave up or concave down?

  7. Assignment • Lesson 2.5 • Page 86 • Exercises 1 – 19 odd

More Related