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Math Help - Rolle's Theorem and the Mean-value Theorem

  1. #1
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    Rolle's Theorem and the Mean-value Theorem

    Show that hes exactly one root in .
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  2. #2
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    Quote Originally Posted by lacy1104 View Post
    Show that hes exactly one root in .
    On the interval (0, 0.5\pi), the function f(x) = x^3 + x^2 + 4x - cos x is negative at x = 0 but positive at x = 0.5\pi. If you can show that the derivative of f(x) is positive for x \in (0, 0.5\pi), then you know that a root exists by the Intermediate Value Theorem, and that it is the only root by the Extreme Value Theorem.
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