Rolles Theorem

  • Thread starter Miike012
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  • #1
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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...
 

Answers and Replies

  • #2
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I don't see any problem with what you said. All polynomials are defined and continuous on the entire real line.
 
  • #3
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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.
 
  • #4
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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."
 
  • #5
LCKurtz
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Assuming you are using standard notation: "If p is a polynomial, then p ε C[a,b]".
 
  • #6
HallsofIvy
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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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