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Math Help - Intermediate Value Theorem

  1. #1
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    Intermediate Value Theorem

    Can somebody help me with this problem. I'm trying to just understand it but having a hard time. Thanks

    Use the Intermediate Value Theorem to show that there is a root of the equation x3+2x2=42 on the interval (0, 3). Your final answer should state your chosen values of N, f(x), a, and b.
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  2. #2
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    IVT: If f is continuous on the interval [a,b] and s is a number between f(a) and f(b), then there exists a number c in the interval [a,b] such that f(c) = s

    For your question, imagine s = 0 (i.e. a root)

    Let f(x) = x^3 + 2x^2 - 42. Note: f(0) = -42 and f(3) = 444. So what can you conclude from IVT?
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  3. #3
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    So anything in between these two points 0 and 3 on the X-axis which will be C, will equal automatically equal S, which is between F(a) and F(b)?
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  4. #4
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    The theorem says that if you give me a number between f(0) and f(3), call it s, I can guarantee you that I will find you a number c in between 0 and 3 such that f(c) = s.

    Put s = 0 and you're done.
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