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Finding the local minimum of a graph

  1. Nov 6, 2011 #1
    1. The problem statement, all variables and given/known data
    The question provides a graph and asks for the local minimums. I attached a picture with the graph.

    2. The attempt at a solution
    I said the local minima are when x=0,2,5.

    However the answer key suggests they are at 1,2,5.
    Could someone please explain why 1 is a local minimum? It is just a point on the graph...
    Maybe the answer key is wrong.
     

    Attached Files:

  2. jcsd
  3. Nov 7, 2011 #2

    ehild

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    Recall how "local minimum" is defined.

    ehild
     
  4. Nov 7, 2011 #3
    So local minimum tells us that a y value near the point is always greater than the y value of the point. That is why we can call it the local minimum. However, in this case the dot is no continuous, so there is no y value near it to compare?

    I understand why 0 cannot be a local minimum but I fail see see why 1 can be.
     
  5. Nov 7, 2011 #4

    ehild

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    Are the y(x) values near to x=1 higher than y(1)? The function does not need to be continuous to have a local minimum.


    ehild
     
  6. Nov 7, 2011 #5
    Ah okay, but what about x=6? Values near it are both lower, isn't that a local minimum then?
     
  7. Nov 7, 2011 #6

    ehild

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    If all values near x=6 are lower than y(6) so y(6) is higher then anything else nearby, is it a minimum???

    ehild
     
  8. Nov 7, 2011 #7

    HallsofIvy

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    No, its a local maximum!
     
  9. Nov 7, 2011 #8

    ehild

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    HallsofIvi,

    I know that you know it, (and I hope you think that I also know it) but I asked the OP...:wink:


    ehild
     
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