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The following question was given on a Calculus midterm test: Use the Intermediate Value Theorem (IVT) to show that the equation x3 - 2x -

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The following question was given on a Calculus midterm test: "Use the Intermediate Value Theorem (IVT) to show that the equation x3 - 2x - 19 = 0 has at least one solution on the interval (1, 4)." A student provided the following solution to this question. "Let f (x) = x3 - 2x - 19. Plugging in endpoints: f(1) = 13 -2.1 - 19 = -20 0. Since the values at the endpoints have different signs, one positive and one negative, by the IVT there exists at least one point c E (1, 4) such that f(c) = 0, which is a solution to this equation." This question was worth 5 points. The student received 4 points for it. Why did he lose a point? Paragraph V BIUA EVEN + v

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