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Homework Help: Trouble with local extrema graph

  1. Oct 29, 2007 #1
    1. The problem statement, all variables and given/known data
    Sketch a graph of a function f that is continuous on [1,5] and has no local maximum and minimum, but 2 and 4 are critical numbers.


    2. Relevant equations



    3. The attempt at a solution
    Knowing 2 and 4 are critical numbers, I formed the base function x[tex]^{}2[/tex]-6x+8. Not sure how to go about sketching the graph the meets the stipulations beyond this.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 29, 2007 #2

    JasonRox

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    Just draw it. No need to actually have a concrete function.
     
  4. Oct 29, 2007 #3

    JasonRox

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    Also, note that x^3 has no maximum or minimum but has a critical point where? What does that point look like?

    Also, are you sure it's [1,5]?
     
  5. Oct 29, 2007 #4
    So just sketch a graph that has no local extrema on [1,5]? If so how are 2 and 4 critical numbers?
     
  6. Oct 29, 2007 #5
    Yes it is [1,5], and x^3 has a critical point at 0, and it has a slope of zero. Correct?
     
  7. Oct 29, 2007 #6
    I still need somewhat of a solid answer here, do I just sketch a graph where x=0 on [1,5] or something different? Any help here would be great.
     
  8. Oct 29, 2007 #7

    Dick

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    You sketch a graph where x=2 and x=4 have horizontal tangents, but aren't maxes or mins.
     
  9. Oct 30, 2007 #8
    does that satisfy the continuity?
     
  10. Oct 30, 2007 #9

    Dick

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    Just draw the curve y=x^3 and look what happens at x=0. Now draw a curve with two points like that.
     
  11. Oct 30, 2007 #10
    how can you do that without creating an extrema?
     
  12. Oct 30, 2007 #11

    Dick

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    Put your pencil on a paper at x=1. Curve up until you reach x=2 then flatten out but don't go down. Increase out of the flat part till you get to x=4, then flatten out again. Then increase some more till you get to x=5.
     
  13. Oct 30, 2007 #12
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