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Find the polynomial

  1. Jun 10, 2013 #1

    utkarshakash

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    1. The problem statement, all variables and given/known data
    Find a polynomial f(x) of degree 4 which increases in the intervals (-∞,1) and (2,3) and decreases in the interval (1,2) and (3,∞) and satisifes the condition f(0)=1

    2. Relevant equations

    3. The attempt at a solution
    Let f(x)=ax^4+bx^3+cx^2+dx+1
    f'(1)=f'(2)=f'(3)=0

    But using the above results I get only 3 eqns whereas there are 4 variables.
     
  2. jcsd
  3. Jun 10, 2013 #2

    ehild

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    You have to find one polynomial from the infinite many which obey the conditions.

    ehild
     
  4. Jun 11, 2013 #3

    utkarshakash

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    I still can't figure out.
     
  5. Jun 11, 2013 #4
    There are a lot of polynomials which satisfy the requirements. Luckily you only need ONE of them, get it?
     
  6. Jun 11, 2013 #5

    HallsofIvy

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    What you are being told is that this problem does NOT have a single, unique, answer. You can use the three equations to solve for three of a, b, c, and d, in terms of the other one. Then just arbitrarily choose a value for that one to get one such polynomial out of the infinite number that satisfy these conditions.
     
  7. Jun 11, 2013 #6

    LCKurtz

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    That doesn't help us to help you. Nor does it show any effort.

    Halls just told you how to work the problem. Have you tried that?
     
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