Consider the following equation. 3x4 8x3 + 2 = 0, [2, 3] %3D (a) Explain...

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Consider the following equation. 3x4 – 8x3 + 2 = 0, [2, 3] %3D (a) Explain how we know that the given equation must have a root in the given interval. Let f(x) = 3x4 - 8x + 2. The polynomial f is continuous on [2, 3], f(2) < 0, and f(3) > 0, so by the Intermediate Value Theorem, there is a numberc in (2, 3) such that f(c) = In other words, the equation 3x4 - 8x + 2 = 0 has a root in [2, 3]. (b) Use Newton's method to approximate the root correct to six decimal places. Consider the following equation. 3x4 – 8x3 + 2 = 0, [2, 3] %3D (a) Explain how we know that the given equation must have a root in the given interval. Let f(x) = 3x4 - 8x + 2. The polynomial f is continuous on [2, 3], f(2) < 0, and f(3) > 0, so by the Intermediate Value Theorem, there is a numberc in (2, 3) such that f(c) = In other words, the equation 3x4 - 8x + 2 = 0 has a root in [2, 3]. (b) Use Newton's method to approximate the root correct to six decimal places.

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