nsider the following. -2x5 + 9x4-7x³ - 12x = 0, [3,4] ) Explain how we know that the given equation must have a solution in the given interval. Let f(x) = -2x5 + 9x4-7x3-12x. The polynomial f is continuous on [3, 4], f(3) =18 f(c) = 0 > 0, and f(4) = -240 ✓ . In other words, the equation -2x5 + 9x4-7x³- 12x = 0 has a solution in [3, 4]. >) Use Newton's method to approximate the solution correct to six decimal places. x = x < 0, so by the Intermediate Value Theorem, there is a number c in (3, 4)

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