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Use the Intermediate Value Theorem to sh...

Use the Intermediate Value Theorem to show that the polynomial function `f(x) = x^(3) + 2x-1` has a zero in the interval [0,1].

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To show that the polynomial function \( f(x) = x^3 + 2x - 1 \) has a zero in the interval \([0, 1]\) using the Intermediate Value Theorem (IVT), we will follow these steps: ### Step 1: Evaluate the function at the endpoints of the interval We need to calculate \( f(0) \) and \( f(1) \). - **Calculate \( f(0) \)**: \[ f(0) = 0^3 + 2(0) - 1 = -1 ...
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Knowledge Check

  • The value of c in Rolle's theorem for the function f(x) = x^(3) - 3x in the interval [0,sqrt(3)] is

    A
    `1`
    B
    `-1`
    C
    `3/2`
    D
    `1/3`

  • The value of c in Rolle's theorem for the function f(x) = x^(3) - 3x in the interval [0,sqrt(3)] is

    A
    `1`
    B
    `-1`
    C
    `3/2`
    D
    `1/3`

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