1 / 5

Critical Points and Local Extrema of a Function

Explore the critical points and local extrema of a function with continuous second derivatives. Determine saddle points, local minimums and local maximums. Find the closest points on a surface to the origin.

asaro
Download Presentation

Critical Points and Local Extrema of a Function

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. Suppose (1, 1) is a critical point of a function f with continuous second derivatives. In the case of {image} what can you say about f? • f has a saddle point at (1,1) • f has a local minimum at (1,1) • f has a local maximum at (1,1)

  2. Find the saddle point of the function {image} • (6, 2) • (3, 4) • (3, 2) • (2, 3)

  3. At what point is the following function a local minimum? {image} • (0,12) • (0,4) • (0,4.5) • (3,4)

  4. Find the critical points of the function. {image} • (-4 ,4 ), (-12 ,12 ),(10 ,-10 ) • (-2 ,10 ), (-10 ,-12 ),(12 ,2 ) • (2 ,2 ), (10 ,10 ),(-12, 0) • (-2 , 2 ), (-10 , 10 ), (12 ,-12 )

  5. Find the points on the surface {image} that are closest to the origin. • (0, 0, -25) • (0, 0, 5) (0, 0, -5) • (0, 0, 25) (0, 0, -25) • (0, 0, 5)

More Related