1 / 11

Applied Calculus (MAT 121) Dr. Day Thursday Feb 16, 2012

Applied Calculus (MAT 121) Dr. Day Thursday Feb 16, 2012. Begin Chapter 4: Applications of the Derivative. What does the first derivative tell us?. Big Ideas

sydnee
Télécharger la présentation

Applied Calculus (MAT 121) Dr. Day Thursday Feb 16, 2012

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. Applied Calculus (MAT 121)Dr. Day Thursday Feb 16, 2012 Begin Chapter 4: Applications of the Derivative MAT 121

  2. MAT 121

  3. What does the first derivative tell us? Big Ideas • The direction a function is moving at any point—how it is changing at that point—is revealed in its derivative, because a function’s derivative gives us instantaneous rate of change (IROC) at a point. This connects with the increasing and decreasing nature of a function. • The peaks and valleys of a function—its maximum and minimum values and where they occur—can often be detected using the derivative. When a smoothly flowing function reaches a max or a min, its tangent line slope can be nothing except 0, because the tangent line is horizontal. MAT 121

  4. Increasing and Decreasing Nature of Functions • What do we mean by increasing and decreasing? • How does the derivative reveal info to indicate whether a function is increasing or decreasing at some point? MAT 121

  5. Where is This Function Increasing? Decreasing? • Connection: Sign of Derivative Direction of Change MAT 121

  6. The First Derivative Reveals Whethera Function is Increasing and Decreasing • Connection: Sign of Derivative Direction of Change MAT 121

  7. The First Derivative Reveals Whethera Function is Increasing and Decreasing Example: Determine the intervals on which the function f(x) = x3 – 3x2 – 24x + 32 is increasing and on which it is decreasing. MAT 121

  8. The First Derivative Reveals Whethera Function is Increasing and Decreasing Example: Determine the intervals on which the function f(x) = x2/3is increasing and on which it is decreasing. MAT 121

  9. The First Derivative Reveals Whethera Function is Increasing and Decreasing Example: Determine the intervals on which the function f(x) = x+ 1/xis increasing and on which it is decreasing. MAT 121

  10. A Function’s Maximum and Minimum Values • <<Insert function images to bring out ideas of max and min.>> • What do we mean by maximum and minimum? • How does the derivative reveal connect with these extreme values? • What is a derivative doesn’t exist at a point? MAT 121

  11. Assignments WebAssign 4.1 due Monday 2/20 Reminder: Check results for Test #2 MAT 121

More Related