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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)

  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?
    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


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    Hi daniel69! :smile:

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


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    Staff Emeritus
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    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.
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