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Show that tan^3(x)-8(tan^2(x))+17(tan(x)0-8 = 0

has a root in [0.5, 0.6]. Apply the Bisection Method twice to find an interval of length 0.025 containing this root.

I have NO idea where to go with that equals 0 part...I could figure it without it but that throws me off can't plug any numbers in

  • calculus -

    If there is a root in [0.5,0.6] then that means that f(.5) * f(.6) < 0

    That is, the graph crosses the axis there somewhere, and the function changes sign.

    f(.5) = -0.9374
    f(.6) = 0.2062

    So, bisect the interval

    f(.55) = -0.3539

    Still negative, so bisect again

    f(.575) = -0.0708

    Still negative, so the root is in [0.575,0.6]

    In fact, it turns out to be 0.5813

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