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Rolles Theorem

  1. Nov 7, 2011 #1
    The first hypothesis is that f is continuous on [a,b]....

    Is there a more concise mathematical way of saying... "because the function f is a polynomial it is continuous in its domain."? Because I rather not write that on my test it looks sloppy and non professional...
     
  2. jcsd
  3. Nov 7, 2011 #2

    Mark44

    Staff: Mentor

    I don't see any problem with what you said. All polynomials are defined and continuous on the entire real line.
     
  4. Nov 7, 2011 #3
    I know but is there another way to state that using math symbols or something to make it more concise in like 2-5 words.
     
  5. Nov 7, 2011 #4

    Mark44

    Staff: Mentor

    This is all you need to say.
    "...because the function f is a polynomial, it is defined and continuous [STRIKE]in its domain[/STRIKE] on the entire real line."
     
  6. Nov 7, 2011 #5

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

    Assuming you are using standard notation: "If p is a polynomial, then p ε C[a,b]".
     
  7. Nov 8, 2011 #6

    HallsofIvy

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    Staff Emeritus
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    Note, by the way, that Rolle's theorem also requires that the function be differentiable on some interval. Fortunately, it is also true that all polynomials are differentiable for all x.
     
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