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Solving for continutity

  1. Sep 23, 2009 #1
    1. The problem statement, all variables and given/known data

    Show the problem f(x)=((x-a)^2)*((x-b)^2) + x take on a value of a+b/2
    for some x?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 23, 2009 #2

    Dick

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    What are f(a) and f(b)?? Can you think of a theorem that might apply??
     
  4. Sep 23, 2009 #3
    Have no idea...
     
  5. Sep 23, 2009 #4

    Dick

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    What are f(a) and f(b)????? Work it out!!
     
  6. Sep 23, 2009 #5
    How do I do that, can you show me.
    Thanks
     
  7. Sep 23, 2009 #6

    Dick

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    Put 'a' in for 'x' into your expression for f(x). The result is f(a). What is it? Start DOING SOMETHING, ok?
     
  8. Sep 23, 2009 #7
    ok, what does that do for you, as get two different answers
     
  9. Sep 23, 2009 #8
    so that gives you (a-b)^2 + a and (b-a)^2 + b
    so what do u do next.
     
  10. Sep 23, 2009 #9
    a^2+b^2 - 2ab and b^2+a^2-2ab +b
     
  11. Sep 23, 2009 #10

    Dick

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    That's not right. Show me how you got those and I'll show you what you did wrong.
     
  12. Sep 23, 2009 #11
    I just put in a for x and b for x, its obvious, what is wrong with it...?
     
  13. Sep 23, 2009 #12
    Could you show me the reasoning, as have no clue how to do the problem, just spinning my wheels.
     
  14. Sep 23, 2009 #13

    Dick

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    f(a)=(a-a)^2*(a-b)^2+a. What's (a-a)^2?
     
  15. Sep 23, 2009 #14
    0 I guess?
     
  16. Sep 23, 2009 #15
    so how do you solve the remainder of the problem then??
     
  17. Sep 23, 2009 #16

    Dick

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    So what does that give for f(a) and f(b)? How are they related to (a+b)/2? To finish it get your book out and look for a theorem about continuous functions that might help. I'll give you a hint. The name of the theorem has the word 'intermediate' in it.
     
  18. Sep 23, 2009 #17
    Sorry still dont get the relationship thing between a+b/2, can you explain further
     
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