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Math Help - Advice on how to solve a continous function

  1. #1
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    Advice on how to solve a continous function

    I have the following homework problem that I do not know how to approach.

    Find c such that function defined piecewise is continuous

    For what value of the constant c is the function f continuous on ( -∞, ∞)

    f(x) = cx^2 + 2x if x<2
    x^3 - cx if x ≥ 2

    In the back of the book the answer is suppose to be 2/3. I would like advice on how to approach and solve this problem. Thanks
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  2. #2
    Eater of Worlds
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    \lim_{x\to 2^{-}}cx^{2}+2x=4c+4

    \lim_{x\to 2^{+}}x^{3}-cx=8-2c

    4c+4=8-2c

    Solve for c and what do you get?.
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  3. #3
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    thanks!
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  4. #4
    Senior Member bkarpuz's Avatar
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    Smile

    Quote Originally Posted by fishguts View Post
    I have the following homework problem that I do not know how to approach.

    Find c such that function defined piecewise is continuous

    For what value of the constant c is the function f continuous on ( -∞, ∞)

    f(x) = cx^2 + 2x if x<2
    x^3 - cx if x ≥ 2

    In the back of the book the answer is suppose to be 2/3. I would like advice on how to approach and solve this problem. Thanks
    The function is defined as follows:
    f(x):=\begin{cases}cx^{2}+2x,&x<2 \\ cx,&x\geq2\end{cases}
    for x\in\mathbb{R}.
    We know that polynomials are continuous functions and thus we see that f is piecewise continuous; that is, f consists of two continuous functions.
    Therefore it suffices to set c in such a way that f is also continuous at the critical point x=2.
    The rest is what galactus has shown.
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