1 / 6

Intervals of Concavity

Unit 4. Intervals of Concavity. Definition. A graph is concave up if it forms a parabola that opens upward A graph is concave down if it forms a parabola that opens downward An inflection point is a point where a graph switches concavity. Example graphs. Concave up. Concave down .

edie
Download Presentation

Intervals of Concavity

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. Unit 4 Intervals of Concavity

  2. Definition A graph is concave up if it forms a parabola that opens upward A graph is concave down if it forms a parabola that opensdownward Aninflection point is a point where a graph switches concavity

  3. Example graphs Concave up Concave down

  4. Example of Inflection Point Point of inflection is at (0,0). This is where the concavities change from up ward to downward. (- ) 8 8 Concave up: , 0) Concave down: ( 0, Point of Inflection: (0,0)

  5. Procedure Find the second derivative Find the critical numbers Where f”(x)=0 Values of x that make f(x) or F”(x) undefined Place those values on a number line Test a value in each interval in the second derivative Concave up where f”(x) is positive Concave down where f”(x) is negative Write the intervals

  6. Examples Concave up: (-1/4, Concave down: ( ,-1/4) Infection point: (-1/4, 29/8) ) 8 8 -1/4

More Related