Consider the following. 3x4 - 8x + 5 = 0, [2, 3) (a) Explain how we know that the given equation must have a solution in the given interval. Let f(x) = 3x* - 8x3 + 5. The polynomial fis continuous on [2, 31, f(2) = 3x - 8x + 5 = 0 has a solution in [2, 3). < 0, and f(3) = > 0, so by the Intermediate Value Theorem, there is a number c in (2, 3) such that f(c) = In other words, the equation (b) Use Newton's method to approximate the solution correct to six decimal places.

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