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Math Help - Intermediate Value Theorem

  1. #1
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    Intermediate Value Theorem

    Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval:

    1. the third root of x = 1-x, (0,1)

    Note: I'd really appreciate it if somebody could tell me how to type in the square root and other root symbols.

    2. cosx = x (0,1)
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  2. #2
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    Quote Originally Posted by dm10 View Post
    Note: I'd really appreciate it if somebody could tell me how to type in the square root and other root symbols.
    \frac{2}{3}

    Code:
    [math]\frac{2}{3}[/math]
    2\sqrt{32}

    Code:
    [math]2\sqrt{32}[/math]

    Mo.
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  3. #3
    MHF Contributor
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    Quote Originally Posted by dm10 View Post
    Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval:

    1. the third root of x = 1-x, (0,1)

    Note: I'd really appreciate it if somebody could tell me how to type in the square root and other root symbols.

    2. cosx = x (0,1)
    1. Use the function f(x) = x^{1/3} + x - 1, and calculate the values for this function at x = 0 and x = 1. What does the Intermediate Value Theorem tell you about this result?

    2. Use the function g(x) = \cos x - x, calculate the value for this function at x = 0, and show that \cos 1 - 1 is negative.
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