1 / 6

Chapter 4 Curve Sketching

Chapter 4 Curve Sketching. Using Derivatives instead of Plotting Points. Lets relate a graph to its derivative. Find the first derivative. Put zeroes on a number line Find the second derivative. Put zeroes on a number line Lets look at the graph here:. Slope. y′ = slope, correct?

odette-rasmussen
Download Presentation

Chapter 4 Curve Sketching

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. Chapter 4 Curve Sketching Using Derivatives instead of Plotting Points

  2. Lets relate a graph to its derivative Find the first derivative. Put zeroes on a number line Find the second derivative. Put zeroes on a number line Lets look at the graph here:

  3. Slope y′ = slope, correct? Logic says (as did the graph): y′ > 0 m+ Graph rises y′ < 0 m– Graph falls y ′ = 0 m = 0 Graph hits peak or valley

  4. Curvature y′′ = curvature We saw on the graph y ′′ > 0 concave up y ′′ < 0 concave down y ′′ = 0 inflection point

  5. Some vocabulary Critical Point where y′ = f′ = 0 or DNE Absolute Maximum f(c) ≥ f(x) for all x in domain (highest point overall) Absolute Minimum f(c) ≤ f(x) for all x in domain (lowest point overall) Relative Maximum/Minimum f(c) ≥ f(x)/f(c) ≤ f(x) for x near c (high or low somewhere in a small area)

  6. How to graph this way? Lets see if we can figure it out, with an example: Please may I have another? Of course you may. 

More Related