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Math Help - continuity and differentiability challenge problem

  1. #1
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    continuity and differentiability challenge problem

    hey guys

    the question is:

    3ax - 7, x<2
    ax^2 + bx + 1, x is greater than or equal to 2

    find a and b so that the function is continuous and differentiable

    i already put them equal to each other but at the end i get a-b = 4

    can someone please help me find out how to solve it, if it is even possible
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  2. #2
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    Re: continuity and differentiability challenge problem

    Quote Originally Posted by ubhutto View Post
    the question is:
    3ax - 7, x<2
    ax^2 + bx + 1, x is greater than or equal to 2
    find a and b so that the function is continuous and differentiable
    i already put them equal to each other but at the end i get a-b = 4
    can someone please help me find out how to solve it, if it is even possible
    If f(x) = \left\{ {\begin{array}{rl}   {3ax,} & {x < 2}  \\   {ax^2  + bx + 1,} & {x \geqslant 2}  \\ \end{array} } \right.

    You need to make \lim _{x \to 2^ -  } f(x) = \lim _{x \to 2^ +  } f(x)\;\& \,\lim _{x \to 2^ -  } f'(x) = \lim _{x \to 2^ +  } f'(x)
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