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Homework Help: Relative Extrema

  1. Mar 3, 2010 #1
    1. The problem statement, all variables and given/known data
    I have to find a, b, c, and d such that the function defined by :
    f(x) = ax3+bx2+cx+d
    will have a relative extrema at points (1,2) and (2,3).

    3. The attempt at a solution
    From the given critical points, I am able to know that when x=1 or x=2, f'(x)=3ax2+2bx+c should be equal to zero.

    Therefore f'(x) should have factors like (x-1) and (x-2) or in simplified form x2-3x+2. Now my problem is that how should I relate the two equations of f'(x) for me to be able to solve for the said unknowns?
     
  2. jcsd
  3. Mar 3, 2010 #2

    Gib Z

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    Well you know f'(x) = 3ax^2 + 2bx + c = 0 when x=1 and x=2, So substitute that in. You will get two equations which you can view as linear equations in the variables a, b, c, d, with the coefficient of d being zero.

    What else do you need to solve this system and how can you get that information?
     
  4. Mar 3, 2010 #3
    >>> after getting the two equations: 3a + 2b + c and 12a + 4b + c, what will I do... I still could not find a way to get the values of a, b, c, and d... after eliminating c, I only get 9a + 2b giving two variables unknown still.. help.. :(
     
  5. Mar 3, 2010 #4

    Gib Z

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    You can get two more equations. Look at all your information again!
     
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