1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Local minima

  1. Apr 15, 2008 #1
    for the equation... y = x^3 - 2x^2 -5x +2

    is its local minima at (2.120,-8.061)

    Thanks
     
  2. jcsd
  3. Apr 15, 2008 #2
    How do you find local minima/maxima? First find all the critical points. HOw do you find critical points?
    1.f'(x)=0
    2.f'(x) does not exist
    since your function is a polynomial it means that also it's derivative will be a polynomial of a less degrees, so it will be defined for all real numbers.

    Now, after you find the cr. points, how do you distinguish whether it is a local minima or a local maxima?
    SInce it is a cubic polynomial there will be max two local extremes.

    Say c,d are such cr. points
    then c is said to be a local minima if: let e>0, such that e-->0

    so f'(c-e)<0,and f'(c+e)>0

    and d i said to be a local max, if

    f'(d-e)>0 and f'(d+e)<0.

    Now do it in particular for your function.

    Can you go from here???
     
  4. Apr 16, 2008 #3
    i just look at the hessian to figure out if it's a min or not
     
  5. Apr 16, 2008 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi daniel69! :smile:

    How did you get x = 2.120 ?
     
  6. Apr 16, 2008 #5
    Look at what?
     
  7. Apr 16, 2008 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Since this is a function of a single variable, its "Hessian" is just its second derivative. However, that would be assuming that the x value given really does give either a maximum or a minimum- which, I think, was part of the question.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Local minima
  1. Maxima minima (Replies: 3)

  2. Global maxima & minima (Replies: 5)

Loading...