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Math Help - Another Differentiable Equation

  1. #1
    Member CalcGeek31's Avatar
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    Another Differentiable Equation

    Okay this one is different. when I take the derivative I assume I can just plug in but I am not sure if it will work.
    f(x)=
    ax^2 + 1/3, x > 1

    bx-10/3, x <1

    I took the limit, and got a +1/3 = b - 10/3, then I took the derivative of the equation and took the same limit and got 2a = b. Do I just plug 2a in for b?
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  2. #2
    Member CalcGeek31's Avatar
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    I am getting 11 but it would be very helpful to me if someone would explain it.
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  3. #3
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    Quote Originally Posted by CalcGeek31 View Post
    Okay this one is different. when I take the derivative I assume I can just plug in but I am not sure if it will work.
    f(x)=
    ax^2 + 1/3, x > 1

    bx-10/3, x <1

    I took the limit, and got a +1/3 = b - 10/3, then I took the derivative of the equation and took the same limit and got 2a = b. Do I just plug 2a in for b?
    What's the original question? Are you being asked to find the values of a and b so that curve is differentiable at x = 1? If so, then what you propose is correct.

    By the way, is ax^2 + 1/3 meant to be ax^2 + \frac{1}{3} or \frac{ax^2 + 1}{3} ....?

    Quote Originally Posted by CalcGeek31 View Post
    I am getting 11 but it would be very helpful to me if someone would explain it.
    11 for what?
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