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Math Help - Differentiable equations

  1. #1
    Member CalcGeek31's Avatar
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    Differentiable equations

    The problem: Find the value of b that makes the function differentiable.

    f(x) =

    ax^2 + 10, x> 2

    x^2 -6x +b, x < 2

    It is a peicewise function just incase that doesn't look right to someone.

    I have attempted setting both functions equalto one another but all I ended up with was b-4a = 2 and I am stuck after that.
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  2. #2
    MHF Contributor
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    the function needs to be continuous ...

    \lim_{x \to 2^-} f(x) = \lim_{x \to 2^+} f(x)

    4 - 12 + b = 4a + 10


    and so does the derivative of f ...

    \lim_{x \to 2^-} f'(x) = \lim_{x \to 2^+} f'(x)

    4 - 6 = 4a
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  3. #3
    Member CalcGeek31's Avatar
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    so then a = -1/2?

    but that makes my b = -1 and for what Im doing it is not possible to have negative answers. Am I just wrong in my calculations?

    Yes I am wrong, I multiplied by -8 instead off subtracting.
    Last edited by CalcGeek31; January 4th 2009 at 10:54 AM. Reason: I can't add
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  4. #4
    MHF Contributor
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    Quote Originally Posted by CalcGeek31 View Post
    so then a = -1/2?

    but that makes my b = -1 and for what Im doing it is not possible to have negative answers. Am I just wrong in my calculations?
    no ... b = 16
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  5. #5
    Member CalcGeek31's Avatar
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    Yes I got that too thank you for your help.
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