1 / 12

Today in Pre-Calculus

Today in Pre-Calculus. Go over homework Notes: Finding Extrema You ’ ll need a graphing calculator Homework. decr: (- ∞ , 0 ) incr: (0 , ∞). incr: (- ∞ , ∞). decr: (- ∞ , 0 ) incr: (0 , ∞). decr: ( 3, ∞ ) incr: (-∞, 0 ) constant: (0, 3). decr: ( 3 , 5 ) incr: (-∞ , 3 )

chul
Download Presentation

Today in Pre-Calculus

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. Today in Pre-Calculus • Go over homework • Notes: Finding Extrema • You’ll need a graphing calculator • Homework

  2. decr: (- ∞, 0 ) incr: (0, ∞) incr: (- ∞, ∞) decr: (- ∞, 0 ) incr: (0, ∞) decr: ( 3, ∞) incr: (-∞, 0 ) constant: (0, 3) decr: ( 3, 5 ) incr: (-∞, 3 ) constant: ( 5, ∞) decr: (- 1, 1) incr: (- ∞, -1 ), ( 1, ∞) decr: (- ∞, ∞) incr: (- ∞, 0) decr: (0, ∞) decr: (2,∞) incr: (-∞,-2) constant(-2,2) decr: (- ∞, -4) incr: ( 4, ∞) Inc(0,3) decr: (- ∞, 0) cons: (3, ∞) decr: ( - ∞, 7)υ (7, ∞)

  3. Extrema • Definition: The peaks and valleys where a graph changes from increasing to decreasing or vice versa. • Types: Minima and Maxima Local (relative) and absolute

  4. Local (or relative) extrema • A local maximum for a function f, is a value f(c) that is greater than or equal to the range values of f on some open interval containing c. • A local minimum for a function f, is a value f(c) that is less than or equal to the range values of f on some open interval containing c.

  5. Absolute extrema • An absolute maximum for a function f, is a value f(c) that is greater than or equal to ALL of the range values of f. • An absolute minimum for a function f, is a value f(c) that is less than or equal to ALL of the range values of f.

  6. Example Relative minimum of -10.75 at x = -2.56 Relative max of 38.6 at x = -0.40 Absolute min of -42.93 at x = 2.21

  7. Example 1 Absolute minimum of -1.688 at x = -1.500

  8. Example 2 Local maximum of 9.481 at x = -1.667 Local minimum of 0 at x = 1

  9. Example 3 Absolute minimum of -11.2 at x = -1.714 Local maximum of 0.459 at x = 0.312 Local minimum of -1.758 at x = 1.402

  10. Example 4 These are absolute because for the min, there are no values in the range less than -1 and for the max, there are no values in the range greater than 1.

  11. Example 5 Absolute minimum of -4 at x = 2 Relative minimum of -1 at x = -3 Relative maximum of 3 at x = 1

  12. Homework • Wkst.

More Related